7.  "ft 


BY  THE  SAME  AUTHOR, 


&£#t-bo0k  an 


FOR  THE  USE  OF  SCHOOLS  AND  COLLEGES, 

WITH    NEARLY   300   ILLUSTRATIONS.       12MO,    SHEEP.       PRICE   75   CENTS. 

(Third  Edition,  revised.) 


TEXT-BOOK 


NATUKAL  PHILOSOPHY. 


FOR   THE    USE    OF 


SCHOOLS  AND  COLLEGES. 


CONTAINING   THE   MOST   RECENT  DISCOVERIES   AND  FACTS   COM- 
PILED FROM  THE  BEST  AUTHORITIES. 


JOHN 'WILLIAM  DRAPER,   M.D., 

PROFESSOR   OF  CHEMISTRY   IN   THE   UNIVERSITY  OF  NEW  YORK,  AND   FORMERLY 

PROFESSOR    OF   NATURAL   PHILOSOPHY  AND   CHEMISTRY   IN   HAMP- 

DEN  SIDNEY  COLLEGE,   VIRGINIA. 


nearly  Jfour  ^untoretr  Xllustratfons* 


NEW    YORK: 
HARPER  &   BROTHERS,   PUBLISHERS, 

82   CLIFF   STREET. 

1847. 


Entered,  according  to  Act  of  Congress,  in  the  year  one  thousand 
eight  hundred  and  forty-seven,  by 

HARPER  &  BROTHERS, 

in  the  Clerk's  Office  of  the  District  Court  of  the  Southern  District 
of  New  York. 


X7 


PREFACE. 


THE  success  which  has  attended  the  publication  of  my 
'*  Text-Book  on  Chemistry,"  four  large  editions  of  it 
having  been  called  for  in  less  than  a  year,  has  induced 
me  to  publish,  in  a  similar  manner,  the  Lectures  I  for- 
merly gave  on  Natural  Philosophy  when  professor  of  that 
science. 

It  will  be  perceived  that  I  have  made  what  may  appear 
an  innovation  in  the  arrangement  of  the  subject ;  and, 
instead  of  commencing  in  the  usual  manner  with  Me- 
chanics, the  Laws  of  Motion,  &c.,  I  have  taught  the 
physical  properties  of  Air  and  Water  first.  This  plan 
was  followed  by  many  of  the  most  eminent  writers  of 
the  last  century ;  and  it  is  my  opinion,  after  an  extensive 
experience  in  public  teaching,  that  it  is  far  better  than 
the  method  ordinarily  pursued. 

The  main  object  of  a  teacher  should  be  to  communi- 
cate a  clear  and  general  view  of  the  great  features  of  his 
science,  and  to  do  this  in  an  agreeable  and  short  manner. 
It  is  too  often  forgotten  that  the  beginner  knows  nothing ; 
and  the  first  thing  to  be  done  is  to  awaken  in  him  an 
interest  in  the  study,  and  to  present  to  him  a  view  of  the 
scientific  relations  of  those  natural  objects  with  which  he 
is  most  familiar.  When  his  curiosity  is  aroused,  he  will 
readily  go  through  things  that  are  abstract  and  forbidding ; 


IV  PREFACE. 

which,  had  they  been  presented  at  first,  would  have  dis- 
couraged or  perhaps  disgusted  him. 

I  am  persuaded  that  the  superficial  knowledge  of  the 
physical  sciences  which  so  extensively  prevails  is,  in  the 
main,  due  to  the  course  commonly  pursued  by  teachers. 
The  theory  of  Forces  and  of  Equilibrium,  the  laws  and 
phenomena  of  Motion,  are  not  things  likely  to  allure  a 
beginner ;  but  there  is  no  one  so  dull  as  to  fail  being 
interested  with  the  wonderful  effects  of  the  weight,  the 
pressure,  or  thje  elasticity  of  the  air.  It  may  be  more 
consistent  with  a  rigorous  course  to  present  the  sterner 
features  of  science  first ;  but  the  object  of  instruction  ib 
more  certainly  attained  by  offering  the  agreeable. 

But  though  this  work  is  essentially  a  text-book  upon  my 
Lectures,  I  have  incorporated  in  it,  from  the  most  recent 
authors,  whatever  improvements  have  of  late  been  intro- 
duced in  the  different  branches  of  Natural  Philosophy, 
either  as  respects  new  methods  of  presenting  facts  or  the 
arrangement  of  new  discoveries.  In  this  sense,  this  work 
is  to  be  regarded  as  a  compilation  from  the  best  authori- 
ties adapted  to  the  uses  of  schools  and  colleges. 

Disclaiming,  therefore,  any  pretensions  to  originality, 
except  where  directly  specified  in  the  body  of  the  work, 
I  ought  more  particularly  to  refer  to  the  treatises  of 
Lame  and  Peschel  as  the  authorities  I  have  chiefly  fol- 
lowed in  Natural  Philosophy ;  to  Arago,  Herschel,  and 
Dick  in  Astronomy.  To  the  treatises  of  M.  Peschel  and 
the  astronomical  works  of  Dr.  Dick  I  am  also  indebted 
for  many  very  excellent  illustrations. 

Those  subjects,  such  as  Caloric,  which  belong  partly 
to  Chemistry  and  partly  to  Natural  Philosophy,  and 
which,  therefore,  have  been  introduced  in  my  text-book 
on  the  former  subject,  I  have  endeavored  to  present  here 
in  a  different  way,  that  those  who  use  both  works  may 
have  the  advantage  of  seeing  the  same  subject  from  dif- 


PREFACE.  V 

ferent  points  of  view.  The  laws  of  Undulations,  now 
beginning  to  be  recognized  as  an  essential  portion  of  this 
department  of  science,  I  have  introduced  as  an  abstract 
of  what  has  been  written  on  this  subject  by  Peschel  and 
Eisenlohr. 

It  will,  therefore,  be  seen  that  the  plan  of  this  work  is 
essentially  the  same  as  that  of  the  Text-Book  on  Chem- 
istry. It  gives  an  abstract  of  the  leading  points  of  each 
lecture  —  three  or  four  pages  containing  the  matter  gone 
over  in  the  class-room  in  the  course  of  an  hour.  The 
lengthened  explanations  and  demonstrations  which  must 
always  be  supplied  by  the  teacher  himself  are,  therefore, 
except  in  the  more  difficult  cases,  here  omitted.  The 
object  marked  out  has  been  to  present  to  the  student  a 
clear  view  of  the  great  facts  of  physical  science,  and 
avoid  perplexing  his  mind  with  a  multiplicity  of  details. 

There  are  two  different  methods  in  which  Natural 
Philosophy  is  now  taught:  —  1st,  as  an  experimental 
science  ;  2d,  as  a  branch  of  mathematics.  Each  has  its 
own  peculiar  advantages,  and  the  public  teacher  will 
follow  the  one  or  the  other  according  as  it  is  his  aim  to 
store  the  mind  of  his  pupil  with  a  knowledge  of  the  great 
facts  of  nature,  or  only  to  give  it  that  drilling  which  arises 
from  geometrical  pursuits.  From  an  extensive  compari-  // 
son  of  the  advantages  of  these  systems,  I  believe  that 
the  proper  course  is  to  teach  physical  science  experi- 
mentally first  —  a  conviction  not  only  arising  from  consid- 
erations respecting  the  constitution  of  the  human  mind, 
the  amount  of  mathematical  knowledge  which  students 
commonly  possess,  but  also  from  the  history  of  these 
sciences.  Why  is  it  that  the  most  acute  mathematicians 
and  metaphysicians  the  world  has  ever  produced  for  two 
thousand  years  made  so  little  advance  in  knowledge,  and  ,/- 


why  have  the  last  two  centuries  produced  such  a 
derful  revolution  in  human  affairs  1     It  is  from  the  lesstm 


VI  PREFACE. 

first  taught  by  Lord  Bacon,  that,  so  liable  to  fallacy  are 
the  operations  of  the  intellect,  experiment  must  always 
be  the  great  engine  of  human  discovery,  and,  therefore, 
of  human  advancement. 

To  teachers  of  Natural  Philosophy  I  offer  this  book  as 
a  practical  work,  intended  for  the  daily  use  of  the  class- 
room, and,  therefore,  so  divided  and  arranged  as  to  en- 
able the  pupil  to  pass  through  the  subjects  treated  of  in 
the  time  usually  devoted  to  these  purposes.  A  great 
number  of  wood  cuts  have  been  introduced,  with  a  view 
of  supplying,  in  some  measure,  the  want  of  apparatus  or 
other  means  of  illustration.  The  questions  at  the  foot  of 
each  page  point  out  to  the  beginner  the  leading  facts 
before  him. 

JOHN  WILLIAM  DRAPER. 


University,  New  York, 
July  16, 1847. 


CONTENTS. 


Lecture                                              -—'•••^   •   i  P«g» 

I.  Properties  of  Matter         .       .       .*       .-.  -.,_*/.  1 

II.  Properties  of  Matter  and  Physical  Forces  .        .'      .  6 

III.  Natural  Philosophy— Pneumatics    .«../*       .  11 

IV.  Weight  and  Pressure  of  the  Air  .       «-—:»>r.       .  17 
V.  Pressure  of  the  Air  ..       .. 22 

VI.  Pressure  and  Elasticity  of  the  Air       .        .        .        .  26 

VII.  Properties  of  Air     ....        .        .        .        .        ;  31 

VIII.  Properties  of  Air  (continued)     "  f  ',    ..'--'«•'     .        .  36 

IX.  Hydrostatics — Properties  of  Liquids       v      \       *  .    .  41 

X.  The  Pressures  of  Liquids    .        ,       ,\\    ...  45 

XI.  Specific  Gravity       .        .        ,      ' «       .        .        .        .50 

XII.  Hydrostatic  Pressure 55 

XIII.  Flowing  Liquids  and  Hydraulic  Machines     .      -."»  -    «'-'.4Q 

XIV.  Theory  of  Flotation :.  '    .  "   i    '  6* 

XV.  Mechanics — Motion  and  Rest  . r'  '; '    -i""'-v  - '*'»       .  69 

XVI.  Composition  and  Resolution  of  Forces       ...  72 

XVII.  Inertia      .        .        .    -V^Vr^l^v  •  ^i  -i .  77 

XVIII.  Gravitation  .        .        .       i  -    „•      »  ^^r     .       .  81 

XIX,. Descent  of  Falling  Bodies      ..  e :: 'kr..  PJ>* M ',   -    ; ..     .  85 

XX.  Motion  on  Inclined  Planes — Projectiles     .        .        .  90 

XXI.  Motion  round  a  Center  »'--.••*;•  *./•;-..;£.       ...  94 

XXII.  Adhesion  and  Capillary  Attraction     .  .-„  .^:-  :;       .  101 

XXIII.  Properties  of  Solids        .        .      :.    ^fci-.-      .        .  107 

XXIV.  Center  of  Gravity      -  ./     ',.     '^:  •  .*  •'  .^  «•  !  .^  no 
XXV.  The  Pendulum        »">•    '  *.      * '--4 'v.;,.  ...V.  .  116 

XXVI.  Percussion 121 

XXVII.  The  Mechanical  Powers— the  Lever     .        .        .        .126 

XXVIII.  The  Pulley— the  Wheel  and  Axle       .        .        .        .  131 

XXIX.  The  Inclined  Plane— Wedge— Screw    .        .        .        .137 

XXX.  Passive  'or  Resisting  Forces        .        .     %               .  141 

XXXI.  Undulatory  Motions        .       '.                .        .        •        .  147 

XXXII.  Undulatory  Motions  (continued)  .        ..     '.       .  '     .  152 

XXXIII.  Acoustics — Production  of  Sound  ...      .„       .       .  157 

XXXIV.  Phenomena  of  Sound  .        .       .        .:-...    .       .  161 
XXXV.  Optics— Properties  of  Light 168 

XXXVI.  Measures  of  the  Intensity  and  Velocity  of  Light      .  172 

XXXVII.  Reflexion  of  Light 178 

XXXVIII.  Refraction  of  Light     .        .        .        .       „      .       .  184 


Vlll  CONTENTS. 

Lecture  Page. 

XXXIX.  Action  of  Lenses 190 

XL.  Colored  Light 195 

XLI.  Colored  Light  (continued) 200 

XLII.  Undulatory  Theory  of  Light 205 

XLIII.  Polarized  Light 210 

XLIV.  Double  Refraction 215 

XLV.  Natural  Optical  Phenomena 221 

XLVI.  The  Organ  of  Vision 227 

XLVIL  Optical  Instruments— Microscopes    .....  232 

XL  VIII.  Telescopes 238 

XLIX.  Thermotics— the  Properties  of  Heat         .        .        .        .244 

L.  Radiant  Heat 249 

LI.  Conduction  and  Expansion        ......  253 

LII.  Capacity  for  Heat  and  Latent  Heat        .        .        .        .  258 

LIII.  Evaporation  and  Boiling 262 

LIV.  The  Steam  Engine 267 

LV.  Hygrometry 272 

LVI.  Magnetism 278 

LVIL  Terrestrial  Magnetism 283 

LVIII.  Electricity 288 

LIX.  Induction  and  Distribution  of  Electricity          *  293 

LX.  The  Voltaic  Battery        .......  298 

LX1.  Electro-magnetism 304 

LXII.  Magneto-electricity — Thermo-electricity        .        .        .  309 

LXIII.  Astronomy 315 

LXIV.  Translation  of  the  Earth  round  the  Sun       ...  321 

LXV.  The  Solar  System *.        .328 

LXVI.  The  Solar  System  (continued)  334 

LXVIL  The  Secondary  Planets 340 

LXVIII.  The  Fixed  Stars 346 

LXIX.  Causes  of  the  Phenomena  of  the  Solar  System       .        .353 

LXX.  The  Tides 358 

LXXI.  Figure  and  Motion  of  the  Earth                                       .  363 

LXXII.  Of  Perturbations 369 

LXXIII.  The  Measurement  of  Time       .  .373 


INTRODUCTION. 

CONSTITUTION    OP    MATTER. 

LECTURE  I. 

PROPERTIES  OF  MATTER.  —  The  Three  Forms  of  Mat- 
ter.—  Vapors. —  The  distinctive,  essential,  and  accessory 
properties. — Extension. — Impenetrability. —  Unchangea- 
bility. — Illustrations  of  Extension. — Methods  of  measur- 
ing small  spaces. —  The  Spherometer. —  Illustration  of 
Impenetrability. —  The  Diving-Bell. 

^MATERIAL  substances  present  themselves  to  us  under 
three  different  conditions.  Some  have  their  parts  so 
strongly  attached  to  each  other  that  they  resist  the  intru- 
sion of  external  bodies,  and  can  retain  any  shape  that 
may  be  given  them.  These  constitute  the  group  of  SOL- 
IDS. A  second  class  yields  readily  to  pressure  or  move- 
ment, their  particles  easily  sliding  over  one  another ;  and 
from  this  extreme  mobility  they  are  unable  of  themselves 
to  assume  determinate  forms,  but  always  copy  the  shape 
of  the  receptacles  or  vessels  in  which  they  are  placed — 
they  are  LIQUIDS.  A  third,  yielding  even  more  easily 
than  the  foregoing,  thin  and  aerial  in  their  character,  and 
marked  by  the  facility  with  which  they  may  be  compress- 
ed into  smaller  or  dilated  into  larger  dimensions,  give  us 
a  group  designated  as  GASES.  Metals  may  be  taken  as 
examples  of  the  first ;  water  as  the  type  of  the  second  ; 
and  atmospheric  air  of  the  third  of  these  states  or  condi- 
tions, "which  are  called  "  the  three  FORMS  of  bodies." 

In  some  instances  the  same  substance  can  exhibit  all 
three  of  these  forms.  Thus,  when  liquid  water  is  cooled 

Under  how  many  states  do  material  substances  occur?  What  are 
solids?  What  are  liquids  ?  What  are  gases?  Give  examples  of  each. 
What  is  the  technical  designation  given  to  these  states  ?  Give  an  exam- 
ple of  a  substance  that  can  assume  all  three  forms. 

A 


2  DISTINCTIVE    PROPERTIES. 

to  a  certain  degree,  it  takes  on  the  solid  condition,  as  ice 
or  snow  ;  and  when  its  temperature  is  sufficiently  raised,  it 
assumes  the  gaseous  state,  and  is  then  known  as  steam. 
Writers  on  Natural  Philosophy  have  found  it  convenient, 
for  many  reasons,  to  introduce  the  term  Vapors,  meaning 
by  that  a  gas  placed  under  such  circumstances  that  it  is 
ready  to  assume  the  liquid  state.  As  the  steam  of  water 
conforms  to  this  condition,  it  is  therefore  regarded  as  a 
vapor. 

Under  whichever  of  these  forms  material  substances  are 
presented,  they  exhibit  certain  properties:  these  are,  first, 
Distinctive  ;  second,  Essential ;  third,  Accessory. 

There  is  a  certain  bright  white  metal  passing  under  the 
name  of  Potassium,  the  distinctive  character  of  which  is, 
Fig.  I.  that,  when  thrown  on  the  surface  of  water,  it 
gives  rise  to  a  violent  reaction,  a  beautiful 
violet-colored  flame  being  evolved.  A  piece 
of  lead,  which,  to  external  appearance,  is 
not  unlike  the  potassium  when  brought  in 
contact  with  water,  exhibits  no  such  phe- 
nomenon, but,  as  every  one  knows,  remains  quietly,  neither 
disturbing  the  water  nor  being  acted  upon  by  it. 

Such  distinctive  qualities  are  the  objects  of  a  Chemist's 
studies.  It  belongs  to  his  science  to  show  how  some  gases 
are  colored  and  others  colorless;  some  supporters  of  com- 
bustion, while  others  extinguish  burning  bodies ;  how  some 
liquids  can  be  decomposed  by  Voltaic  batteries  and  some 
by  exposure  to  a  red  heat.  The  general  doctrines  of  af- 
finity, the  modes  in  which  bodies  combine,  and  the  char- 
acters of  the  products  to  which  they  give  rise — all  these 
belong  to  Chemistry. 

But  beyond  these  distinctive  qualities  of  bodies,  there 
are,  as  has  been  observed,  certain  other  properties  which 
are  uniformly  met  with  in  all  bodies  whatever,  and  hence 
are  spoken  of  as  ESSENTIAL.  TThey  are, 

Extension. 

Impenetrability. 

Unchangeability. 

By  EXTENSION  we  mean  that  all  substances,  whatever 

Into  what  classes  may  the  properties  of  bodies  be  divided  ?  Give  an  ex- 
ample of  distinctive  properties.  What  is  the  object  of  the  science  of 
Chemistry?  What  are  the  essential  properties  of  bodies?  What  is 
meant  by  extension  ?  What  by  impenetrability  ? 


ESSENTIAL    PROPERTIES. 


their  volume  or  figure  may  be,  occupy  a  determinate  por- 
tion of  space,  We  measure  them  by  three  dimensions — 
length,  breadth,  and  thickness. 

IMPENETRABILITY  points  out  the  fact  that  two  bodies 
cannot  occupy  the  same  space  at  the  same  time.  If  a  nail 
is  driven  into  wood,  it  enters  only  by  separating  the  woody 
particles  from  each  other;  if  it  be  dropped  into  water,  it 
does  not  penetrate,  but  displaces  the  watery  particles  : 
and  even  in  the  case  of  aerial  bodies,  through  which 
masses  can  move  with  apparently  little  Fig.  2. 

resistance,  the  same  observation  holds 
good.  Thus,  if  we  take  a  wide-mouthed 
bottle,  a,  Fig.  2,  arid  insert  through  its 
cork  a  funnel,  b,  with  a  narrow  neck,  and 
also  a  bent  tube,  c,  which  dips  into  a  glass 
of  water,  d,  on  pouring  any  liquid  into 
the  funnel,  so  that  it  may  fall  drop  by  drop 
into  the  bottle,  we  shall  find,  as  this  takes 
place,  that  air  passes  out,  bubble  after  bubble,  through 
the  water  in  d.  The  air  is,  therefore,  not  penetrated  by 
the  water,  but  displaced. 

The  same  fact  may  also  be  proved  by 
taking  a  cupping-glass,  a.  Fig.  3,  and  im- 
mersing it,  mouth  downward,  in  a  glass  of 
water,  b.  If  the  aperture,  c,  of  the  cup- 
ping-glass be  left  open  the  air  will  rush  out 
through  it,  and  the  water  flow  in  below  : 
but  if  it  be  closed  by  the  finger,  as  the  air 
can  now  no  longer  escape,  the  water  is  un- 
able to  enter  and  occupy  its  place. 

Similar  experiments  establish  the  impenetrability  of 
liquids  by  solids.  If  in  a  glass  of  water,  Fig.  4,  Fig.  4. 
a  leaden  bullet  is  immersed,  it  will  be  seen  that 
as  the  bullet  is  introduced  the  water  rises  to  a 
higher  level,  showing,  therefore,  that  a  liquid  can 
no  more  be  penetrated  by  a  solid  than .  as  was  seen 
in  the  former  experiment,  can  a  gas  by  a  liquid. 
Two  bodies  cannot  occupy  the  same  space  at  the  same 
time. 

The  third  essential  property  of  matter  is  its  UNCHANGE- 

Give  an  illustration  that  air  is  not  penetrable  by  water.  Give  an  illus- 
tration of  the  displacement  of  air  by  water.  What  is  meant  by  unchange- 
ability  as  a  property  of  bodies  ?  < 


4  UNCHANGEABILITY    OF    MATTER. 

ABILITY.  This  property  may  be  looked  upon  as  the  foun- 
dation of  Chemistry  ;  and  though  there  are  many  phenom- 
ena which  we  constantly  witness  which  seem  to  contradict 
it,  they  form,  when  properly  considered,  striking  illustra- 
tions of  the  great  truth  that  material  substances  can  nei- 
ther be  created  nor  destroyed,  and  that  the  distinctive 
qualities  which  appertain  to  them  remain  forever  un- 
changed. The  disappearance  of  oil  in  the  combustion  of 
lamps,  the  burning  away  of  coal,  the  evaporation  of  wa- 
ter, when  minutely  examined,  far  from  proving  the  per- 
ishability of  matter,  afford  the  most  striking  evidence  of 
its  duration.  Nor  is  a  solitary  fact  known  in  the  whole 
range  of  Chemistry,  Natural  Philosophy,  or  Physiology, 
which  lends  the  remotest  countenance  to  the  opinion  that, 
either  by  the  slow  lapse  of  time  or  by  any  artificial  pro- 
cesses whatever,  can  matter  be  created,  changed,  or  de- 
stroyed. Even  the  bodies  of  men  and  animals,  the  struct- 
ures of  plants,  and  all  other  objects  in  the  world  of  organ- 
ization, which  seem  characterized  by  the  facility  with 
which  they  undergo  unceasing  and  eventually  total  change, 
are  no  exception  to  the  truth  of  this  observation.  The 
bodies  which  we  possess  to-day  are  made  up  of  particles 
which  have  formed  the  bodies  of  other  animals  in  former 
times,  and  which  will  again  discharge  the  same  duty  for 
races  that  will  hereafter  come  into  existence. 

As  illustrations  connected  with  the  extension  and  im- 
penetrability of  matter,  I  may  give  the  following  in- 
stances : 

We  are  frequently  required  to  measure  the  dimensions 
of  bodies ;  that  is,  to  determine  their  length,  breadth,  or 
thickness.  It  is  a  much  more  difficult  thing  to  do  this  ac- 
curately than  is  commonly  supposed.  It  requires  an  artist 
of  the  highest  skill  to  make  a  measure  which  is  a  foot  or 
a  yard  in  length,  or  which  shall  contain  precisely  a  pint  or 
a  gallon.  With  a  view  of  facilitating  the  measurement  of 
bodies,  a  great  many  contrivances  have  been  invented, 
such  as  verniers,  spherometers,  and  screw  machines  of 
different  kinds. 

The  spherometer,  which  is  a  beautiful  contrivance  for 
measuring  the  thickness  of  bodies,  is  constructed  as  foi- 


ls there  any  reason  to  believe  that  new  material  particles  can  be  ere 
ated  by  artificial  processes,  or  old  ones  destroyed  ? 


THE    SPHERO.METER. 


Fig  5. 


lows  :  It  has  three  horizontal  steel  branches,  a,  &,  c,  Fig. 
5,  which  form  with  each  other 
angles  of  120  degrees.  From  the 
extremities  of  these  branches 
there  proceed  three  delicate  steel 
feet,  d,  e,f,  and  through  the  cen- 
ter, where  the  branches  unite,  a 
screw,  g,  the  thread  of  which  is 
cut  with  great  precision,  and 
which  terminates  in  a  pointed 
foot,  «,  passes.  The  head  of  this 
screw  carries  a  divided  circle,  m. 
Now,  suppose  the  instrument  is 
placed  on  a  piece  of  flat  glass,  it 
will  be  supported  on  its  three 
feet,  which  are  all  in  the  same  plane ;  but  if  in  turning  the 
screw  we  depress  its  point,  i,  beneath  the  plane  of  its  feet, 
it  can  no  longer  stand  with  stability  on  the  glass,  but  tot- 
ters when  it  is  touched,  and  emits  a  rattling  sound.  By 
altering  the  screw,  therefore,  we  can  give  it  such  a  posi- 
tion that  both  by  the  finger  and  the  ear  we  discover  that 
its  point  is  level  with  the  points  d,  e,f.  Now  let  the  ob- 
ject, the  thickness  of  which  is  to  be  measured,  be  placed 
on  the  glass,  and  the  screw  turned  until  the  instrument 
stands  without  tottering,  it  is  obvious  that  its  point  must 
have  been  lifted  through  a  distance  precisely  equal  to 
the  thickness  of  the  object  to  be  measured,  and  the 
movement  of  the  head  of  the  screw  read  off  upon  the 
scale,  n,  against  which  it  works,  indicates  what  that  thick- 
ness is. 

This  instrument,  therefore,  serves  to  show  that  in  the 
measurement  of  small  spaces,  the  senses  of  touch  and 
hearing  may  often  be  resorted  to  with  more  effect  than 
the  eye.  The  spherometer  is  here  introduced  in  connec- 
tion with  these  general  considerations  respecting  the  ex- 
tension of  matter,  as  affording  the  student  an  illustration 
of  the  delicate  methods  we  possess  of  determining  the  mi- 
nutest dimensions  of  bodies. 

As  an  illustration  of  the  impenetrability  of  matter,  the 
machine  which  passes  under  the  name  of  the  diving-bell 


Describe  the  spherometer.    What  is  its  use  ?    By  what  senses  may  we 
often  form  a  better  estimate  of  small  spaces  than  by  the  eye  ? 


6  ACCESSORY    PROPERTIES. 

may  be  mentioned.     It  consists  of  a  vessel,  <z,  a,  Fig.  6, 
Fig.  6.  of  any  suitable  shape,  and  heavy  enough 

to  sink  in  water  when  plunged  with  its 
mouth  downward.  Owing  to  the  impen- 
etrability of  the  air  the  water  is  excluded 
from  the  interior,  or  only  finds  access  to 
such  an  extent  as  corresponds  to  the  press- 
ure of  the  depth  to  which  it  is  sunk. 
Light  is  admitted  to  the  bell  through  thick 
pieces  of  glass  in  its  top,  and  a  constant 
stream  of  fresh  air  thrown  into  it  from  a 
tube,  b,  and  forcing-pump  above,  the  at- 
mosphere in  the  inside  being  suffered  to  escape  through 
a  stop-cock  as  it  becomes  vitiated  by  the  respiration  of 
the  workmen.  Diving-bells  are  extensively  resorted  to 
in  submarine  architecture,  and  for  the  recovery  of  treas- 
ure lost  in  the  sea. 


LECTURE  II. 

PROPERTIES  OF  MATTER. —  The  Accessory  Properties  of 
Matter. —  Compressibility. — Expansibility. — Elasticity. 
— Limit  of  Elasticity. — Illustrations  of  Divisibility. — 
Porosity  and  interstitial  spaces. —  Weight. 

PHYSICAL  FORCES. — Attractive  and  Repulsive  Forces. — 
Molecular  Attraction. — Gravitation . — Cohesion. — Con- 
stitution of  Matter. 

HAVING  disposed  of  the  essential,  we  pass  next  to  a  con- 
sideration of  the  accessory  properties  of  matter.  They  are, 

'  Compressibility. 
Expansibility. 
-   Elasticity. 
Divisibility. 
Porosity. 
Weight. 

That  substances  of  all  the  three  forms  are  compressi- 
ble is  capable  of  easy  proof.  In  the  process  of  coining, 
pieces  of  metal  are  exposed  to  powerful  pressure  between 
the  steel  die's',  sO  that  they  become  much  denser  than  be- 

Describe  the  diving-bell.  On  what  principle  does  it  act  ?  Why  must 
the  air  in  its  interior  be  renewed  from  time  to  time  ?  What  are  the  acces- 
soiy  properties  of  matter? 


EXPANSIBILITY    AND    ELASTICITY.  7 

fore.  By  inclosing  water  or  any  other  liquid  in  a  strong 
vessel,  and  causing  a  piston,  driven  by  a  screw,  to  act 
upon  it,  it  may  be  reduced  to  a  less  space,  and  gaseous 
substances,  such  as  atmospheric  air  when  inclosed  in  an 
India-rubber  bag,  or  even  a  bladder,  may  be  compressed 
by  the  hands. 

Under  the  influence  of  heat  all  substances  expand. 
This  may  be  proved  for  such  solids  Ff^.  7. 

as  metals  by  the  apparatus  represent- 1  j^^^^^^^^^jl 
ed  in  Fig.  7.  It  consists  of  a  stout  I  aT  <*^l 

board,  a  bt  on  which  are  fastened  two  ^ 
brass  uprights,  c,  d,  with  notches  cut  in  them  so  as  to  re- 
ceive the  ends  of  a  metallic  bar,  e.  This  bar  is  slightly 
shorter  than  the  whole  distance  between  the  notches,  so 
that  when  it  is  set  in  its  place  it  can  be  moved  backward 
and  forward,  and  emits  a  rattling  sound.  But  if  boiling 
water  be  poured  upon  it,  it  expands  and  occupies  the 
whole  distance,  and  can  no  longer  be  moved.  The  ex- 
pansion of  liquids  is  well  shown  in  the  case  of  common 
thermometers,  which  contain  either  quicksilver  or  spirits 
of  wine — those  substances  occupying  a  greater  volume  as 
their  temperature  rises.  The  air  thermometer  proves  the 
same  thing  for  gases. 

By  elasticity  we  mean  that  quality  by  which  bodies, 
when  their  form  has  been  changed,  endeavor  to  recover 
their  original  shape.  In  this  respect  there  are  great  dif- 
ferences. Steel,  ivory,  India-rubber  are  highly  elastic, 
and  lead,  putty,  clay  less  so.  Perfectly  elastic  bodies  re- 
sist the  action  of  disturbing  causes  without  any  ulterior 
change:  thus  a  quantity  of  atmospheric  air,  compressed 
into  a  copper  globe,  recovers  its  original  volume  as  soon 
as  the  pressure  is  removed,  though  it  may  have  been  shut 
up  for  years.  By  the  limit  of  elasticity  we  mean  the 
smallest  force  which  is  required  to  produce  a  permanent 
disturbance  in  the  structure  of  an  imperfectly  elastic 
body.  No  solid  is  perfectly  elastic.  An  iron  wire,  drawn 
a  little  aside,  recovers  its  original  straightness  ;  but  if 
more  violently  bent,  it  takes  a  permanent  set,  because  its 
limit  of  elasticity  is  overpassed.  The  elasticity  of  a  given 

Give  proofs  that  solids,  liquids,  and  gases  are  all  compressible.  How 
can  it  be  proved  that  solids,  liquids,  and  gases  are  expansible  ?  What  is 
meant  by  elasticity  ?  Give  examples  of  highly  elastic  and  less  elastic 
bodies.  What  is  meant  by  the  limit  of  elasticity  ? 


8  DIVISIBILITY. 

substance  can  often  be  altered  by  mechanical  processes, 
such  as  by  hammering,  or  by  heating  and  cooling,  as  in 
the  process  of  tempering. 

The  divisibility  of  matter  maybe  proved  in  many  ways. 
By  various  mechanical  processes  metals  may  often  be  re- 
duced to  an  extreme  degree  of  tenuity :  thus  it  is  said 
that  gold-leaf  may  be  beaten  out  until  it  is  only  ^oVo^  °^ 
an  inch  thick.  By  chemical  experiments  a  grain  of  cop- 
per or  of  iron  may  be  divided  into  many  millions  of  parts. 
For  certain  purposes  artists  have  ruled  parallel  lines 
upon  glass,  with  a  diamond  point,  so  close  to  each  other 
that  ten  thousand  are  contained  in  a  single  inch.  The 
odors  which  are  exhaled  by  strong- smelling  perfumes,  as 
musk,  will  for  years  together  infect  the  air  of  a  large 
room,  and  yet  the  loss  of  weight  by  the  musk  is  imper- 
ceptible. Again,  there  are  animals  whose  bodies  are  so 
minute  that  they  can  only  be  seen  by  the  aid  of  the  mi- 
croscope. The  siliceous  shells  of  such  infusorials  occur 
in  many  parts  of  the  earth  as  fossils.  Ehrenberg  has 
shown  that  Tripoli,  a  mineral  used  in  the  arts,  is  made 
up  of  these — a  single  cubic  inch  of  it  containing  about 
forty-one  thousand  millions — that  is,  about  fifty  times  as 
many  individuals  as  there  are  of  human  beings  on  the  face 
of  the  globe. 

As  substances  of  all  kinds  may  be  reduced  to  smaller 
dimensions,  either  by  pressure  or  the  influence  of  cold, 
and  as  it  is  impossible  for  two  particles  to  occupy  the 
same  place  at  the  same  time,  or  even  for  one  of  them  par- 
tially to  encroach  on  the  position  occupied  by  the  other, 
it  necessarily  follows  that  there  must  be  pores  or  inter- 
stices even  in  the  densest  bodies.  Thus  quicksilver  will 
readily  soak  into  the  pores  of  gold,  and  gases  ooze  through 
India-rubber.  Writers  on  Natural  Philosophy  usually 
restrict  the  term  "pore"  to  spaces  which  are  visible  to 
the  eye,  and  designate  those  minute  distances  which  sep- 
arate the  ultimate  particles  of  bodies  by  the  term  "  inter- 
stices." 

All  bodies  have  weight  or  gravity.     It  is  this  which 

How  may  the  elasticity  of  a  given  substance  be  changed  ?  Give  some 
illustrations  of  the  great  divisibility  of  matter,  derived  from  mechanical, 
chemical,  physiological,  and  geological  facts.  How  may  it  be  proved  that 
all  bodies  are  porous?  What  is  meant  by  a  "pore,"  and  what  by  "inter- 
stices ?" 


FORCES    OF    ATTRACTION    AND    REPULSION.  9 

causes  them  to  fall,  when  unsupported,  to  the  ground,  or 
when  supported,  to  exert  pressure  upon  the  supporting 
body.  Nor  is  this  property  limited  to  terrestrial  objects  ; 
for  in  the  same  way  that  an  apple  tends  to  fall  to  the  earth, 
so  too  does  the  moon;  and  all  the  planets  gravitate  to- 
ward each  other  and  toward  the  sun.  It  was  the  consid- 
eration of  this  principle  that  led  M.  LEVERRIER  to  the  dis- 
covery of  a  new  planet  beyond  Uranus — this  latter  star 
being  evidently  disturbed  in  its  movements  by  the  influ- 
ences of  a  more  distant  body  hitherto  unknown. 

OF  PHYSICAL  FORCES. — All  changes  taking  place  in 
the  system  of  nature  are  due  to  the  operation  of  forces. 
The  attractive  force  of  the  earth  causes  bodies  to  fall,  and 
a  similar  agency  gives  rise  to  the  shrinking  of  substances — 
their  parts  coming  closer  together  when  they  are  exposed 
to  the  action  of  cold.  In  like  manner,  when  an  ivory 
ball  is  suffered  to  drop  on  a  marble  slab,  its  particles, 
which  have  been  driven  closer  to  one  another  by  the  force 
of  the  blow,  instantly  recover  their  original  positions  by 
repelling  one  another  ;  that  is  to  say,  through  the  agency 
of  a  repulsive  force.  Of  the  nature  of  forces  we  know- 
nothing.  Their  existence  only  is  inferred  from  the  effects 
they  produce ;  and  according  to  the  nature  of  those  ef- 
fects, we  divide  them  into  ATTRACTIVE  and  REPULSIVE 
FORCES — the  former  tending  to  bring  bodies  closer  to- 
gether, the  latter  to  remove  them  farther  apart. 

It  has  been  found  convenient  to  divide  attractive  forces 
into  three  groups,  according  as  the  range  of  their  action 
or  the  circumstances  of  their  development  differ.  When 
the  attractive  influence  extends  only  to  a  limited  space,  it 
is  spoken  of  as  molecular  attraction  ;  but  the  attraction  of 
gravitation  is  felt  throughout  the  regions  of  space.  By 
cohesion  is  meant  an  attractive  influence  called  into  ex- 
istence when  bodies  are  brought  to  touch  one  another.  It 
is  to  be  understood  that  these  are  only  conventional  dis- 
tinctions; and  it  is  not  improbable  that  all  the  phenomena 
of  attraction  are  due  to  the  agency  of  one  common  cause. 

Chemists  have  shown  that,  in  all  probability,  material 
substances  are  constituted  upon  one  common  type.  They 

What  is  meant  by  weight  or  gravity  ?  Is  it  limited  to  terrestrial  ob- 
jects ?  What  is  meant  by  forces  ?  How  many  varieties  of  them  are  there  ? 
Into  what  three  groups  are  attractive  forces  divided  ?  What  is  the  dis- 
tinction between  them  ? 

»# 


10  NATURE    OF    ATOMIC    FORCES. 

are  made  up  of  minute,  indivisible  particles,  called  atoms, 
which  are  arranged  at  variable  distances  from  each  other. 
These  distances  are  determined  by  the  relative  preva- 
lence of  attractive  and  repulsive  forces,  resident  in  or 
among  the  particles  themselves  ;  and  so  too  is  the  form 
of  the  resulting  mass.  If  the  cohesive  predominates  over 
the  repulsive  force,  a  solid  body  is  the  result ;  if  the  two 
are  equal  it  is  a  liquid,  and  if  the  repulsive  prevails  it 
is  a  gas. 

There  are  many  reasons  which  lead  us  to  suppose  that 
the  repulsive  force,  which  thus  tends  to  keep  the  particles 
of  matter  asunder,  is  the  agent  otherwise  known  as  heat. 
Whenever  the  temperature  of  a  body  rises  it  enlarges  in 
volume,  because  its  constituent  particles  move  from  each 
other,  and  on  the  temperature  falling  the  reverse  effect 
ensues.  If,  as  many  very  eminent  philosophers  believe, 
heat  and  light  are  in  reality  the  same  agent,  it  follows,  by 
a  necessary  consequence,  as  will  be  gathered  from  what 
we  shall  hereafter  have  to  say  on  optics,  that  the  atoms  of 
bodies  vibrate  unceasingly,  and  that  instead  of  there  be- 
ing that  perfect  quiescence  among  them  which  a  superfi- 
cial examination  suggests,  all  material  substances  are  the 
seat  of  oscillatory  movements,  many  millions  of  which  are 
executed  in  the  space  of  a  single  second  of  time  ;  the 
number  increasing  as  the  temperature  rises,  and  dimin- 
ishing as  it  falls. 

What  is  the  true  constitution  of  material  substances?  What  are  the 
forces  residing  among  the  particles  of  bodies  ?  What  are  the  conditions 
which  determine  the  solid,  liquid,  and  gaseous  forms  ?  What  is  probably 
the  nature  of  the  force  of  molecular  repulsion?  If  light  and  heat  are  trie 
same  agent,  what  is  the  condition  of  the  particles  of  bodies  ? 


PNEUMATICS. 


NATURAL  PHILOSOPHY, 


PROPERTIES  OF  THE  AIR. 

PNEUMATICS. 

LECTURE  III. 

NATURAL  PHILOSOPHY. —  Observations  on  this  branch  of 
Science. 

PNEUMATICS. — General  Relations  of  the  Air. — Its  connec- 
tion with  Motion  and  Organization. — Limited  Extent. 
—  Constitution. —  Compressibility. — Causes  which  Limit 
the  Atmosphere. — Its  Variable  Densities. — Proportion- 
ality of  its  Elastic  Force  and  Pressure. 

A  VERY  superficial  knowledge  of  those  parts  of  the 
world  to  which  man  has  access  readily  leads  to  their  class- 
ification under  three  separate  heads — the  air,  the  sea,  and 
the  solid  earth.  This  was  recognized  in  the  infancy  of 
science,  for  the  four  elements  of  antiquity  were  the  di- 
visions which  we  have  mentioned,  and  fire. 

NATURAL  PHILOSOPHY  or  PHYSICAL  SCIENCE,  which,  in 
its  extended  acceptation,  means  the  study  of  all  the  phe- 
nomena of  the  material  world,  may  commence  its  inves- 
tigations with  any  objects  or  any  facts  whatever.  By  pur- 
suing these,  in  their  consequences  and  connections,  all  the 
discoveries  which  the  human  mind  has  made  in  this  de- 
partment of  knowledge  might  successively  be  brought 
forward.  But  when  we  are  left  to  select  at  pleasure  our 
point  of  commencement,  it  is  best  to  follow  the  most  nat- 
ural and  obvious  course.  All  the  advances  made  in  our 
times  by  the  most  eminent  philosophers,  and  our  powers 
of  appreciating  and  understanding  them,  depend  on  clear- 
ness of  perception  of  the  great  fundamental  facts  of  sci- 
ence— a  perspicuity  which  can  never  arise  from  mere  ab- 
stract reasonings  or  from  the  unaided  operations  of  the 

What  were  the  elements  of  the  ancients  ?  What  is  Natural  Philosophy  ? 


12  RELATIONS  OF    THE    ATMOSPHERE. 

human  intellect,  but  which  is  the  natural  consequence  of 
a  familiarity  with  absolute  facts.  These  serve  us  as  our 
points  of  departure,  and  in  the  more  difficult  regions  of 
science  they  are  our  points  of  reference — often  by  their 
resemblances,  and  even  by  their  differences,  making  plain 
what  would  otherwise  be  incomprehensible,  and  spread- 
ing a  light  over  what  would  otherwise  be  obscure. 

In  the  three  divisions  of  material  objects,  which  are  so 
strikingly  marked  out  for  us  by  nature,  we  find  traits  that 
are  eminently  characteristic.  All  our  ideas  of  perma- 
nence and  duration  hiave  a  convenient  representation  in 
the  solid  crust  of  the  earth,  the  mountains,  and  valleys, 
and  shores  of  which  retain  their  position  and  features  un- 
altered for  centuries  together.  But  the  air  is  the  very  type 
and  emblem  of  variety,  and  the  direct  or  indirect  source 
of  almost  every  motion  we  see.  It  scarce  ever  presents 
to  us,  twice  in  succession,  the  same  appearance ;  for  the 
winds  that  are  continually  traversing  it  are,  to  a  proverb, 
inconstant,  and  the  clouds  that  float  in  it  exhibit  every 
possible  color  and  shape.  It  is,  in  reality,  the  grand  ori- 
gin or  seat  of  all  kinds  of  terrestrial  motions.  Storms  in 
the  sea  are  the  consequences  of  storms  in  the  air,  and  even 
the  flowing  of  rivers  is  the  result  of  changes  that  have 
transpired  in  the  atmosphere. 

But  the  interest  connected  with  it  is  far  from  ending 
here.  The  atmosphere  is  the  birthplace  of  all  those" 
numberless  tribes  of  creation  which  constitute  the  vege- 
table and  animal  world.  It  is  of  materials  obtained  from 
it  that  plants  form  their  different  structures,  and,  therefore, 
from  it  that  all  animals  indirectly  derive  their  food.  It  is 
the  nourisher  and  supporter  of  life,  and  in  those  process- 
es of  decay  which  are  continually  taking  place  during 
the  existence  of  all  animals,  and  which  after  death  totally 
resolve  their  bodies  into  other  forms,  the  air  receives  the 
products  of  those  putrefactive  changes,  and  stores  them 
up  for  future  use.  And  it  is  one  of  the  most  splendid 
discoveries  of  our  times,  that  these  very  products  which 
arise  from  the  destruction  of  animals  are  those  which  are 
used  to  support  the  life  and  develop  the  parts  of  plants. 
They  pass,  therefore,  in  a  continual  circle,  now  belong- 
ing  to  the  vegetable,  and  now  to  the  animal  world ; 

What  appears  to  be  the  leading  characteristic  of  the  atmosphere  ?  What 
are  its  relations  to  the  organic  world  ? 


EXTENT    OF    THE   ATMOSPHERE.  13 

they  come  from  the  air,  and  to  it  they  again  are  re- 
stored. 

It  is  not,  therefore,  the  beautiful  blue  color  which  the 
air  possesses,  and  which  people  commonly  call  the  sky, 
or  the  points  of  light  which  seem  to  be  in  it  at  night,  or 
the  moving  clouds  which  overshadow  it  and  give  it  such 
varied  and  fantastic  appearances,  or  even  those  more  im- 
posing relations  which  bring  it  in  connection  with  the 
events  of  life  and  death,  which  alone  invest  it  with  a  pe- 
culiar claim  on  the  attention  of  the  student.  Connected 
as  it  is  with  the  commonest  every-day  facts,  it  furnishes 
us  with  some  of  our  most  appropriate  illustrations — those 
simple  facts  of  reference  of  which  I  have  already  spoken, 
and  to  which  we  involuntarily  turn  when  we  come  to  in- 
vestigate the  more  difficult  natural  phenomena. 

Astronomical  considerations  show  that  the  atmosphere 
does  not  extend  to  an  indefinite  region,  but  surrounds  the 
earth  on  all  sides  to  an  altitude  of  about  fifty  miles.  Com- 
pared with  the  mass  of  the  earth  its  volume  is  quite  insig- 
nificant ;  for  as  it  is  nearly  four  thousand  miles  from  the 
surface  to  the  center  of  the  earth,  the  whole  depth  of  the 
atmosphere  is  only  about  one-eightieth  part  of  that  dis- 
tance. Upon  a  twelve-inch  globe,  if  we  were  to  place  a 
representation  of  the  atmosphere,  it  would  have  to  be  less 
than  the  tenth  of  an  inch  thick. 

Seen  in  small  masses,  atmospheric  air  is  quite  colorless 
and  perfectly  transparent.  Compared  with  water  and 
solid  substances,  it  is  very  light.  Its  parts  move  among 
one  another  with  the  utmost  facility.  Chemists  have 
proved  that  it  is  not,  as  the  ancients  supposed,  an  ele- 
mentary body,  but  a  mixture  of  many  other  substances. 
It  is  enough  at  present  for  us  to  know  that  its  leading 
constituents  are  two  gases,  which  exist  in  it  in  fixed  quan- 
tities— they  are  oxygen  and  nitrogen — but  other  essential 
ingredients  are  present  in  a  less  proportion,  such  as  car- 
bonic acid  gas,  and  the  vapor  of  water. 

Atmospheric  air  is  taken  by  natural  philosophers  as 
the  type  of  all  gaseous  bodies,  because  it  possesses 
their  general  properties  in  the  utmost  perfection.  In- 
dividual gases  have  their  special  peculiarities — some,  for 

What  is  the  altitude  of  the  atmosphere?  What  comparison  does  this 
bear  to  the  mass  of  the  earth  ?  What  are  its  general  properties  ?  What 
bodies  constitute  it  ?  Of  what  class  is  it  the  type  ? 


14  COMPRESSIBILITY    OF    AIR. 

example,  are  yellow,  some  green,  some  purple,  and  some 
red. 

The  first  striking  property  of  atmospheric  air  which  we 
encounter,  is  the  facility  with  which  the  volume  of  a  given 
quantity  of  it  can  be  changed.  It  is  highly  compressible 
and  perfectly  elastic.  A  quantity  of  it  tied  tightly  up  in 
a  bladder  or  India-rubber  bag,  is  easily  forced,  by  the 
pressure  of  the  hand,  into  a  less  space.  The  materiality 
of  the  air,  and  its  compressibility,  are  simultaneously  il- 
lustrated by  the  experiment  of  the  diving-bell,  described 
under  Fig.  6.  A  vessel  forced  with  its  mouth  downward 
under  water,  permits  the  water  to  enter  a  little  way,  be- 
cause the  included  air  goes  into  smaller  dimensions 
under  the  pressure ;  but  as  soon  as  the  vessel  is  again 
brought  to  the  surface  of  the  water,  the  air  within  it  ex- 
pands to  its  original  bulk. 

Fig.  8.  This  ready  compressibility  and  expansibility  may 
be  shown  in  many  other  ways.  Thus,  if  we  take 
a  glass  tube,  Fig.  8,  with  a  bulb  c,  at  its  upper 
end,  the  lower  end  being  open  and  dipping  into  a 
i|  vessel  of  water,  d,  and  having  previously  partially 
filled  the  tube  with  water  to  the  height,  a,  it  will  be 
found,  on  touching  the  bulb  with  snow,  or  by  pour- 
ing on  it  ether,  or  by  cooling  it  in  any  manner,  that 
the  included  air  collapses  into  a  less  bulk.  It  is 
therefore  compressible,  and  on  warming  the  bulb 
with  the  palm  of  the  hand,  the  air  is  at  once  dilated. 

It  is  this  quality  of  easy  expansibility  and  compressi- 
bility which  distinguishes  all  gaseous  substances  from  sol- 
ids and  liquids.  It  is  true  the  same  property  exists  in 
them,  but  then  it  is  to  a  far  less  degree.  On  the  hypoth- 
esis that  material  bodies  are  formed  of  particles  which  do 
not  touch  one  another,  but  are  maintained  by  attractive 
and  repulsive  forces  at  determinate  distances,  it  would 
appear  that,  in  a  gas  like  atmospheric  air,  the  repulsive 
quality  predominates  over  the  attractive ;  while  in  solids 
the  attractive  force  is  the  most  powerful,  arid  in  liquids 
the  two  are  counterbalanced. 

Again,  as  respects  relative  weight,  the  gases,  as  a 
tribe,  are  by  far  the  lightest  of  bodies ;  and,  indeed,  it  is 

How  may  it  be  proved  to  be  compressible  ?  What  does  the  diving-bell 
prove  ?  Describe  the  experiment,  Fig.  8.  In  gaseous  bodies  does  the  at- 
tractive or  repulsive  force  predominate  ? 


ELASTICITY    OF    AIR. 


15 


among  them  that  we  find  the  lightest  substance  in  nature 
— hydrogen  gas.  They  are1,  moreover,  the  only  perfectly 
elastic  substances  that  we  know.  Thus,  a  quantity  of  at- 
mospheric air  compressed  into  a  metal  reservoir  will  re- 
gain its  original  volume  the  moment  it  has  the  opportuni- 
ty, no  matter  how  great  may  be  the  space  of  time  since 
it  was  first  shut  up. 

Under  a  relaxation  of  pressure  this  perfect  elasticity 
displays  itself  in  producing  the  expansion  of  a      fig.  9. 
gas.     If  a  bladder  partially  full  of  atmospheric 
air  be  placed  under  an  air-pump  receiver,  as  the 
pressure  is  removed  it  dilates  to  its  full  extent, 
and  might  even  be  burst  by  the  elastic  force  of 
the  air  confined  within.     The  force  with  which 
this  expansion  takes  place  is  very  well  display- 
ed by  putting  the  bladder  in  a  frame,  as  shown  in  Fig. 
10,  and  loading  it  with  heavy  weights  ;  as  it       Fig.  10. 
expands  by  the  spring  of  the  air,  it  lifts  up  all 
the  weights. 

If  we  were  to  imagine  a  given  volume  of 
gas  placed  in  an  immense  vacuum,  or  under 
such  circumstances  that  no  extraneous  agen- 
cy could  act  upon  it,  it  is  very  clear  that  its 
expansion  would  be  indefinitely  great — the 
repulsive  force  of  its  own  particles  predom- 
inating over  their  attraction,  and  there  being  nothing  to 
limit  their  retreat  from  one  another.  But  when  a  gas- 
eous mass  surrounds  a  solid  nucleus,  the  case  is  different 
— an  expansion  to  a  determinate  and  to  a  limited  extent 
is  the  result.  And  these  are  the  circumstances  under 
which  the  earth  and  every  planet  surrounded  by  an  elas- 
tic atmosphere  exists  ;  for  in  the  same  way  that  our  globe 
compels  an  unsupported  body  to  fall  to  its  surface,  and 
makes  projectiles  as  bomb-shells  and  cannon-shot — no 
matter  what  may  have  been  the  velocity  with  which  they 
were  urged — return  to  the  ground,  so  the  same  attractive 
force  restrains  the  indefinite  expansion  of  the  air,  and 
keeps  the  atmosphere,  instead  of  diffusing  away  into  empty 
space,  imprisoned  all  round. 

Besides  this  cause — gravitation  to  the  earth — a  second 

Are  gases  perfectly  elastic  ?  What  does  experiment  Fig.  9  prove  ?  What 
would  happen  to  a  volume  of  gas  placed  in  an  indefinite  vacuum  ?  What 
limits  the  atmosphere  to  the  earth  ? 


16  VARIABLE    DENSITY    OP   THE   ATMOSPHERE. 

one,  for  the  limited  extent  of  the  atmosphere,  may  also 
be  assigned — contraction — 'sensing  from  cold.  Observa- 
tion has  shown  that,  as  we  rise  to  greater  altitudes  in  the 
air,  the  cold  continually  increases ;  and  gases,  in  common 
•with  all  other  forms  of  body,  are  condensed  by  cold. 
The  attempt  at  unlimited  expansion  which  the  atmos- 
phere, by  reason  of  its  gaseous  constitution  exerts,  is, 
therefore,  kept  in  bounds  by  two  causes — the  attractive 
force  of  the  earth  and  cold — and  accordingly  its  altitude 
does  not  exceed  fifty  miles. 

From  the  circumstance  that  air  is  thus  a  compressible 
body,  we  might  predict  one  of  the  leading  facts  respect- 
ing the  constitution  of  the  atmosphere— it  is  of  unequal 
densities  at  different  heights.  Those  portions  of  it  which 
are  down  below  have  to  bear  the  weight  of  the  whole  su- 
perincumbent mass  ;  but  this  weight  necessarily  becomes 
less  and  less  as  we  advance  to  regions  which  are  higher 
and  higher;  for  in  those  places,  as  there  is  less  air  to  press, 
the  pressure  must  be  less.  And  all  this  is  verified  by  ob- 
servation. The  portions  which  rest  on  the  ground  are  of 
the  greatest  density,  and  the  density  steadily  diminishes 
as  we  rise.  Moreover,  a  little  consideration  will  assure 
us  that  there  is  a  very  simple  relation  between  the  press- 
ure which  the  air  exerts  and  its  elastic  force.  Consider 
the  condition  of  things  in  the  air  immediately  around  us  : 
if  its  elastic  force  were  less,  the  weight  of  the  superincum- 
bent mass  would  crush  it  in ;  if  greater,  the  pressure 
could  no  longer  restrain  it,  and  it  would  expand.  It  fol- 
lows, therefore,  in  the  necessity  of  the  case,  that  the  elas- 
tic force  of  any  gas  is  neither  greater  nor  less,  but  pre- 
cisely equal  to  the  pressure  which  is  upon  it. 

What  is  the  agency  of  cold  in  this  respect  ?  Why  is  the  atmosphere  of 
unequal  density  at  different  heights  ?  What  relation  is  there  between  its 
pressure  and  its  elastic  force  ? 


THE    AIR-PUMP. 


17 


Fig.  11. 


LECTURE  IV. 

WEIGHT  AND  PRESSURE  OF  THE  AIR. — Description  of  the 
Air-pump.- — Its  Action.  —  Limited  Exhaustion.  —  Fun- 
damental fact  that  Air  has  weight. — Relative  weight  of 
other  Gases.  —  Weight  gives  rise  to  Pressure. — Experi- 
ments illustrating  the  Pressure  of  the  Air. 

Ix  the  year  1560,  Otto  Guericke,  a  German,  invented  an 
instrument  which,  from  its  use,  passes  under  the  name  of 
the  air-pump,  and  exhibited  a  number  of  very  striking 
experiments  before  the  Emperor  Ferdinand  III.  This 
incident  forms  an  epoch  in  physical  science. 

Otto  Guericke's  instrument  was  imperfect  in  construc- 
tion and  difficult  of  management.  The  apparatus  re- 
quired to  be  kept  under  water.  More  convenient  ma- 
chines have,  therefore,  been  devised.  The  following  is  a 
description  of  one  of  the  most  simple  :  Upon  a  metallic 
basis,  //,  Fig.  11, 
are  fastened  two  ex- 
hausting syringes,  a 

a,  which  are  worked 
by  means  of  ahandle, 

b,  the  two  screw  col- 
umns, d  d,  aided  by 
the  cross-piece,  e  e, 
tightly   compressing 
them  into  their  pla- 
ces.    A  jar,  c,  called 
a  receiver,  the  mouth 
of  which  is  carefully 
ground  true,  is  pla- 
ced on  the  plate  of 

the  pump,  f  f,  which  is  formed  of  a  piece  of  metal  or 
glass  ground  quite  flat.  This  pump-plate  is  perforated  in 
its  center,  from  which  air-tight  passages  lead  to  the  bot- 

When  and  by  whom  was  the  air-pump  invented  ?  Give  a  description  of 
its  general  external  appearance.  What  is  the  receiver  ?  What  is  the 
pump-plate  ?  What  passages  lead  from  the  center  of  the  plate  ?  What 
is  the  use  of  the  screw  g  ? 


18 


STRUCTURE    OF    THE    AIR-PUMP. 


Fig.  12. 


torn  of  each  syringe,  and  when  the  handle,  b,  is  moved 
the  syringes  withdraw  the  air  from  the  interior  of  the  jar. 
From  the  same  central  perforation  there  is  a  third  pass- 
age, which  can  be  opened  or  closed  by  the  screw  at  g,  so 
that  when  the  experiments  are  over,  by  opening  it  the  air 
can  be  readmitted  into  the  interior  of  the  receiver. 

So  far  as  its  exterior  parts  are  concerned,  this  air-pump 
consists  of  a  pair  of  syringes  worked  by  a  handle,  and 
producing  exhaustion  of  the  interior  of  a  jar,  with  a  vent 
which  can  be  closed  or  opened  for  the  readmission  of  air. 
The  syringes  are  constructed 
exactly  alike.  The  glass  model 
represented  in  Fig.  12  exhibits 
their  interior;  each  consists  of  a 
cylinder,  a  a,  the  interior  of  which 
is  made  perfectly  true,  so  that  a 
piston  or  plunger,  d,  introduced  at 
the  top  may  be  pushed  to  the  bot- 
tom, and,  indeed,  work  up  and 
v  down  without  any  leakage.  There 
\X\  is  a  hole  made  through  the  piston, 
d,  and  over  it  a  valve  is  laid.  This 
consists  of  a  flexible  piece  of  mem- 
brane, as  leather,  silk,  &c.,  which 
being  placed  on  the  aperture  opens 
in  one  direction  and  closes  in  the 
other.  Such  a  valve  is  in  the  pis- 
ton, and  there  is  another  one,  c,  resting  on  an  aperture  in 
the  bottom  of  the  cylinder. 

To  understand  the  action  of  this  instrument,  let  us  sup- 
pose a  glass  globe  full  of  atmospheric  air  to  be  fastened 
air-tight  to  the  bottom  of  such  a  syringe,  and  the  piston 
then  lifted  to  the  top  of  the  cylinder.  As  it  moves  with- 
out leakage,  it  would  evidently  leave  a  vacuum  below  it 
were  it  not  that  the  air  in  the  globe,  exerting  its  elastic 
force,  pushes  up  the  valve  c,  arid  expands  into  the  cylin- 
der. In  this  way,  therefore,  by  the  upward  movement  of 
the  piston,  a  certain  quantity  of  air  comes  out  of  the  globe 
and  fills  the  cylinder.  The  piston  is  now  depressed:  the 
moment  it  begins  to  descend,  the  valve  c,  which  leads 

What  are  the  parts  of  each  syringe  ?  How  many  valves  has  it  ?  Which 
way  do  they  open  ?  Describe  what  takes  place  during  the  upward  motion 
of  the  piston.  What  takes  place  during  the  downward  motion  ? 


STRUCTURE    OF    THE    AIR-PUMP.  19 

into  the  globe  shuts ;  and  now  as  the  piston  comes  down 
it  condenses  the  air  below  it,  and  as  this  air  is  condensed 
it  resists  exerting  its  elastic  force.  The  piston-valve,  d, 
under  these  circumstances,  is  pushed  open,  and  the  com- 
pressed air  gets  away  into  the  atmosphere.  As  soon  as 
the  piston  has  reached  the  bottom  of  the  cylinder  all  the 
air  has  escaped,  and  the  process  is  repeated  precisely  as 
before.  The  action  in  the  syringe  is,  therefore,  to  draw 
out  from  the  globe  a  certain  quantity  of  air  at  each  up- 
ward movement,  and  expel  this  quantity  into  the  air  at 
each  downward  movement. 

For  reasons  connected  with  the  great  pressure  of  the 
air,  and  also  for  expediting  the  process  of  exhaustion,  two 
syringes  are  commonly  used.  To  their  pistons  are  at- 
tached rods  which  terminate  in  racks,  b  b ;  between 
these  there  is  placed  a  toothed  wheel,  which  is  turned  on 
its  axis  by  the  handle,  its  teeth  taking  into  the  teeth  of 
the  racks.  When  the  handle  is  set  in  motion  and  the 
wheel  made  to  revolve,  it  raises  one  of  the  pistons,  and  at 
the  same  time  depresses  the  other.  The  ends  of  these 
racks  are  seen  in  Fig.  12.  The  wheel  is  included  in  the 
transverse  wooden  bar,  e  e,  Fig.  11. 

By  the  aid  of  this  invaluable  machine  numerous  striking 
and  important  experiments  may  be  made.  The  form  de- 
scribed here  is  one  of  the  most  simple,  and  by  no  means 
the  most  perfect.  For  the  higher  purposes  of  science 
more  complicated  instruments  have  been  contrived,  in 
which,  with  the  utmost  perfection  of  workmanship,  the 
valves  are  made  to  open  by  the  movements  of  the  pump 
itself,  and  do  not  require  to  be  lifted  by  the  elastic  force 
of  the  air.  In  such  pumps  a  far  higher  degree  of  rare- 
faction can  be  obtained. 

No  air-pump,  no  matter  how  perfect  it  may  be.  can 
ever  make  a  perfect  vacuum,  or  withdraw  all  the  air  from 
its  receiver.  The  removal  of  the  air  depends  on  the  ex- 
pansion of  what  is  left  behind,  and  there  must  always  be 
that  residue  remaining  which  has  forced  out  the  portion 
last  removed  by  the  action  of  the  syringes. 

The  fundamental  fact 'in  the  science  of  Pneumatics  is, 
that  atmospheric  air  is  a  heavy  body,  and  this  may  be 

How  are  the  pistons  rftoved  by  the  rack  ?  What  contrivances  are  intro- 
duced in  the  more  perfect  air-pumps  ?  Can  any  of  these  instruments 
make  a  perfect  vacuum  ?  What  is  the  cause  of  this  ? 


WEIGHT    OF    THE    AIR. 


proved  in  a  very  satisfactory  manner  by  the  aid  of  the 
Fig.  13.  pump.     Let    there   be    a   glass 

flask,  a,  Fig.  13,  the  mouth  of 
which  is  closed  with  a  stop-cock, 
through  which  the  air  can  be  re- 
moved. If  from  this  flask  we  ex- 
haust all  the  air,  and  then  equi- 
poise  it  with  weights  at  a  balance 
as  soon  as  the  stop-cock  is  open- 
ed and  the  air  allowed  to  rush  in 
the  flash  preponderates.  By  add- 
ing weights  in  the  opposite  scale, 
we  can  determine  how  much  it 
requires  to  bring  the  balance 
back  to  equilibrio,  and  there- 
fore what  is  the  weight  of  a  vol- 
ume of  air  equal  to  the  capacity 
of  the  flask. 

Upon  the  same  principles  we 
can  prove  that  all  gases,  as  well 
as  atmospheric  air,  have  weight. 
It  is  only  requisite  to  take  the  exhausted  flask,  and  hav- 
ing counterpoised  it  as  before, 
screw  it  on  to  the  top  of  a  jar, 
c,  Fig.  14,  containing  the  gas 
to  be  tried.  On  opening  the 
stop-cocks,  e  d,  the  gas  flows 
out  of  the  jar  and  fills  the  flask, 
which,  being  removed,  may  be 
again  counterpoised  at  the  bal- 
ance, and  the  weight  of  the  gas 
filling  it  determined.  There  are 
very  great  differences  among 
gases  in  this  respect.  Thus, 
if  we  take  one  hundred  cubic 
inches  of  the  following  they  will  severally  weigh  : 

Hydrogen 2-1  grains. 

Nitrogen 30'1       " 

Atmospheric  air 31-0      " 

Carbonic  acid 47-2      " 

Vapor  of  Iodine 269-8      " 

What  is  the  fundamental  fact  in  Pneumatics  ?  flow  may  the  weight  of 
the  air  he  proved  ?  How  do  other  gases  compare  with  it  in  this  respect  ? 
Mention  some  of  them. 


Fig.  14. 


PRESSURE   OF    THE    AIR.  21 

From  the  fact  that  the  air  has  weight,  it  necessarily 
follows  that  it  exerts  pressure  on  all  those  portions  that 
are  in  the  lower  regions,  having  to  sustain  the  weight 
of  the  masses  above.  And  not  only  does  this  hold  good 
as  respects  the  aerial  strata  themselves,  it  also  holds 
for  all  objects  immersed  in  the  air.  In  most  cases,  the 
resulting  pressure  is  not  detected,  because  it  takes  effect 
equally  in  all  directions,  and  pressures  that  are  equal  and 
opposite  mutually  neutralize  each  other. 

But  when  by  the  air-pump  we  remove  the  pressure 
from  one  side  of  a  body,  and  still  allow  it  to  be  exerted 
on  the  other,  we  see  at  once  abundant  Fis- 

evidence  of  the  intensity  of  this  force. 
Thus,  if  we  take  a  jar,  Pig.  15,  open  at 
both  ends,  and  having  placed  it  on  the 
pump-plate,  lay  the  palm  of  the  hand 
on  the  mouth  of  it ;  on  exhausting  the 
air  the  hand  is  pressed  in  firm  contact 
with  the  jar,  so  that  it  cannot  be  lifted  without  the  exer- 
tion of  a  very  considerable  force. 

In  the  same  way,  if  we  tie  over  a  jar  a  piece  of  blad- 
der, and  allow  it  to  dry,  it  assumes,  of  course,  a  perfectly 
horizontal  position  ;  but  on  exhausting  the  air  within  very 
slightly,  it  becomes  deeply  depressed,  and  is 
soon  burst  inward  with  a  loud  explosion.  This 
simple  instance  illustrates,  in  a  very  satisfacto- 
ry way,  the  mode  in  which  the  pressure  of  the 
air  is  thus  rendered  obvious ;  for  so  long  as 
the  jar  was  not  exhausted,  and  had  air  in  its 
interior,  the  downward  pressure  of  the  atmosphere  could 
not  force  the  bladder  inward,  nor  disturb  its  position  in 
any  manner :  for  any  such  disturbance  to  take  place  the 
pressure  must  overcome  the  elastic  force  of  the  air  with- 
in, which  resists  it,  pressing  equally  in  the  opposite  way 
But  on  the  removal  of  the  air  from  the  interior,  the  press- 
ure above  is  no  longer  antagonized,  and  it  takes  effect 
at  once  by  crushing  the  bladder. 

Why  does  the  air  exert  pressure  ?  What  follows  on  removing  the  press- 
ure from  one  side  of  a  body  ?  Describe  the  experiment  in  Figs.  15  and  16. 
Why  is  not  the  bladder  crushed  in  until  the  air  is  exhausted  ? 


PRESSURE    OP    THE    AIR. 


LECTURE  V. 

THE  PRESSURE  OF  THE  Am.—  The  Magdeburg  Hemis- 
pheres.—  Water  supported  by  Air.  —  The  Pneumatic 
Trough. 

THE  BAROMETER. — Description  of  this  Instrument. — Cause 
of  its  Action. — Different  kinds  of  Barometers. — Meas- 
itrement  of  Accessible  Heights. 

MANY  beautiful  experiments  establish  the  fact  that  the 
atmosphere  presses,  not  only  in  the  downward  direc- 
tion, but  also  in  every  other  way.  Thus,  if  we  take  a  pair 
Fig.  17  of  hollow  brass  hemispheres,  a  b,  Fig.  17,  which 
fit  together  without  leakage,  by  means  of  a  flange, 
and  exhaust  the  air  from  their  interior  through  a 
stop-cock  affixed  to  one  of  them,  it  will  be  found 
that  they  cannot  be  pulled  apart,  except  by  the 
exertion  of  a  very  great  force.  Now  it  does  not 
matter  whether  the  handles  of  these  hemispheres 
are  held  in  the  position  represented  in  the  fig- 
ure, or  turned  a  quarter  way  round,  or  set  at  any  an- 
gle to  the  horizon  they  adhere  with  equal  force  togeth- 
er; and  the  same  power  which  is  required  to  pull  them 
asunder  in  the  vertical  direction,  must  also  be  exerted  in 
all  others.  This,  therefore,  proves  that  the  pressure  of 
the  air  takes  effect  equally  in  every  direction,  whether  up- 
ward, or  downward,  or  laterally. 

In  Fig.  18  a  very  interesting  experiment  is  rep- 
resented. We  take  a  jar,  a,  an  inch  or  two  wide 
and  two  or  three  feet  long,  closed  at  one  end  and 
open  at  the  other,  and  having  filled  it  entirely  with 
water,  place  over  its  mouth  a  slip  of  writing  pa- 
per, b.  If  now  the  jar  be  inverted  in  the  position 
represented  in  the  figure,  it  will  be  seen  that  the 
column  of  fluid  is  supported,  the  paper  neither 
dropping  off  nor  the  water  flowing  out.  This 
remarkable  result  illustrates  the  doctrine  of  the  up- 
ward pressure  of  the  air.  Nor  does  it  even  require  that 

Prove  that  the  air  presses  equally  every  way.    Describe  the  apparatus 
in  Fig.  18.    Why  does  not  the  paper  fall  from  the  mouth  of  the  jar  T 


PRESSURE    OF    THE    AIR. 


23 


Fig.  20. 


a  piece   of  paper  should  be  used  provided  the  glass  has 

the  proper  form.     Thus,  let  there  be  a  bottle,  a,    F*g- 19. 

Fig.  19,  in  the  bottom  of  which  there  is  a  large 

aperture,  b.     If  the  bottle  be  filled  with  water, 

and  its  mouth  closed  by  the  finger,  the  water  will 

not  flow  out,  but  remain  suspended.     And  that 

this  result  is  due  to  the  upward  pressure  of  the 

air  is  proved  by  moving  the  finger  a  little  on 

one  side,  so  as  to  let  the  air  exert  its  pressure  on  the  top 

as  well  as  the  bottom  of  the  water,  which  immediately 

flows  out. 

If  we  take  ajar,  a,  Fig.  20,  and  having  filled  it  full  of 
water,  invert  it  as  is  represented,  in  a 
reservoir  or  trough :  for  the  reason  ex- 
plained in  reference  to  Fig.  18,  the 
water  will  remain  suspended  in  the 
jar.  Such  an  arrangement  forms  the 
pneumatic  trough  of  chemists.  It  en- 
ables them  to  collect  the  various  gas- 
es without  intermixture  with  atmos- 
pheric air ;  for  if  a  pipe  or  tube 
through  which  such  a  gas  is  coming  be  depressed  beneath 
the  moiith  of  the  jar  a,  so  that  the  bubbles  may  rise  into 
the  jar,  they  will  displace  the  water,  and  be  collected  in 
the  upper  part  without  any  admixture. 

If  in  this  experiment  we  use  mercury  instead  of  water, 
the  same  phenomenon  ensues — the  mercury  being  support- 
ed by  the  pressure  of  the  air.  Now  it  might  be  inquired, 
as  the  atmosphere  only  extends  to  a  certain  altitude,  and 
therefore  presses  with  a  weight  which,  though  great,  must 
necessarily  be  limited,  whether  that  pressure  could  sus- 
tain a  column  of  mercury  of  an  unlimited  length  ?  If  we 
take  a  jar  a  yard  in  length,  and  fill  it  with  mercury,  and 
invert  it  in  a  trough,  it  will  be  seen  that  the  mercury  is 
not  supported,  but  that  it  settles  from  the  top  and  de- 
scends until  it  reaches  a  point  which  is  about  thirty  inches 
above  the  level  of  the  mercury  in  the  trough.  Of  course, 
as  nothing  has  been  admitted,  there  must  be  a  vacant 


Will  the  same  take  place  without  any  paper?  Prove  that  it  is  due  to 
the  upward  pressure  of  the  air.  What  is  the  pneumatic  trough?  On 
what  principle  does  it  depend  ?  Will  the  same  take  place  if  mercury  is 
used  instead  of  water?  What  takes  place  when  the  jar  is  more  than  thirty 
inches  high  ? 


24  THE    BAROMETER. 

space  or  vacuum  between  the  top  of  the  mercury  and  the 
top  of  the  jar. 

Fig.  21.  This  experiment  which,  as  we  are  soon  to  see, 
is  a  very  important  one,  is  commonly  made  with 
a  tube,  a  b,  Fig.  21,  instead  of  a  jar — the  tube 
being  more  manageable  and  containing  less  mer- 
cury. It  should  be  at  least  thirty-two  inches  long, 
and  being  filled  with  quicksilver,  may  be  inverted 
in  a  shallow  dish  containing  the  same  metal,  c.  It 
is  convenient  to  place  at  one  side  of  the  tube  a 
scale,  d,  divided  into  inches,  these  inches  being 
counted  from  the  level  of  the  mercury  in  the  dish, 
c.  Such  an  instrument  is  called  a  Barometer,  or 
measurer  of  the  pressure  of  the  air. 

Let  us  briefly  investigate  the  agencies  which  operate 
in  the  case  of  this  instrument.  If,  having  closed  the  mouth 
of  the  tube  b  with  the  finger,  we  lift  it  out  of  the  dish  c, 
it  will  be  found  that  we  must  exert  a  considerable  degree 
offeree  in  order  to  sustain  the  column  of  mercury,  which 
presses  against  the  finger  with  its  whole  weight,  and  tends 
to  push  it  away.  Consequently,  the  mercury  is  continu- 
ally exerting  a  tendency  to  flow  out,  and  therefore  two 
forces  are  in  operation  :  on  the  one  hand,  the  weight  of 
the  mercury  attempting  to  flow  out  of  the  tube  into  the 
dish  ;  and  on  the  other,  the  weight  or  pressure  of  the  at- 
mosphere attempting  to  push  the  mercury  up  in  the  tube. 
Fig.  29.  If  the  pressure  of  the  air  were  greater,  it  would 
push  the  mercury  higher;  if  less,  the  mercury 
would  flow  out  to  a  corresponding  extent.  Thus, 
the  length  of  the  mercurial  column  equilibrates 
the  pressure  of  the  air,  and  we  therefore  say  that 
the  atmospheric  pressure  is  equal  to  so  many 
inches  of  mercury. 

That  the  whole  thing  depends  on  the  pressure 
of  the  air  may  be  beautifully  proved  by  putting 
the  barometer  under  a  tall  air-pump  receiver,  as 
represented  in  Fig.  22,  and  exhausting.  As  the 
pressure  of  the  air  is  reduced  the  mercurial  col- 
umn falls  ;  and  if  it  were  possible  to  make  a  per- 

How  is  this  experiment  commonly  made  ?  Describe  a  barometer.  What 
are  the  forces  which  operate  in  this  instrument  ?  What  does  the  mercu- 
rial column  equilibrate  ?  What  is  it  equal  to  ?  How  may  it  be  proved  to 
depend  on  the  pressure  of  the  air  ? 


THE    BAROMETER.  25 

feet  vacuum  by  such  means,  the  mercury  would  sink  in 
the  tube  to  its  level  in  the  dish.  On  readmitting  the  air 
the  mercury  rises  again,  and  when  the  original  pressure 
is  regained  it  stands  at  the  original  level. 

There  are  many  different  forms  of  barometers,  Fig.  23. 
such  as  the  straight,  the  syphon,  &c.,  but  the  prin- 
ciple of  all  is  the  same.  The  scale  must  uni- 
formly commence  at  the  level  of  the  mercury  in 
the  reservoir.  Now  it  is  plain  that  this  level 
changes  with  the  height  of  the  column ;  for  if 
the  metal  flows  out  of  the  tube  it  raises  the  level 
in  the  reservoir,  and  vice  versa.  In  every  per- 
fect barometer,  means,  therefore,  should  be  had 
to  adjust  the  beginning  of  the  scale  to  the  level 
for  the  time  being.  In  some  barometers,  as  in 
that  represented  in  Fig.  23,  this  is  done  by  hav- 
ing the  mercury  in  a  cistern  with  a  movable  bot- 
tom, and  by  turning  the  screw  V,  the  level  can  be 
precisely  adjusted  to  that  of  the  ivory  point,  a. 

A  barometer  kept  in  the  same  place  under- 
goes variations  of  altitude,  some  of  which  are  reg- 
ular and  others  irregular.  The  former,  which 
depend  on  diurnal  tides  in  the  atmosphere,  anal- 
ogous to  tides  in  the  sea,  occur  about  the  same 
time  of  the  day — the  greatest  depression  being 
commonly  about  four  in  the  morning  and  eve- 
ning, and  the  greatest  elevation  about  ten  in  the 
morning  and  night.  In  summer,  however,  they 
occur  an  hour  or  two  earlier  in  the  morning,  and 
as  much  later  at  night.  The  irregular  changes  depend 
on  meteorological  causes,  and  are  not  reduced  as  yet  to 
any  determinate  laws.  In  amount  they  are  much  more 
extensive  than  the  former,  extending  from  the  twenty-sev- 
enth to  more  than  the  thirtieth  inch,  while  those  are  lim- 
ited to  about  the  tenth  of  an  inch. 

A  very  valuable  application  of  the  barometer  is  for  the 
determination  of  accessible  heights.  The  principle  upon 
which  this  depends  is  simple — the  barometer  necessarily 

What  would  ensue  if  a  perfect  vacuum  could  be  made  ?  What  takes 
place  on  readmitting  the  air?  From  what  point  should  the  scale  of  the 
barometer  commence?  What  are  the  regular  barometric  changes?  What 
is  the  extent  of  the  irregular  ones  ?  How  is  the  barometer  applied  to  the 
measurement  of  heights  ? 

B 


26  MEASURE    OF    ATMOSPHERIC   PRESSURE. 

standing  at  a  lower  point  as  it  is  carried  to  a  higher  posi- 
tion. In  practice  it  is  more  complicated,  and  to  obtain  ex- 
act results  various  methods  have  been  given  by  Laplace, 
Baily,  Littrow,  and  others. 


LECTURE  VI. 

THE  PRESSURE  OF  THE  AIR. — Measure  of  the  Force  with 
which  the  Air  presses. — Different  Modes  of  Estimating 
it. — Experiments  Illustrating  this  Force. 

ELASTICITY  OF  THE  AIR. — Experimental  Illustrations. — 
The  Condenser. 

HAVING,  in  the  preceding  lecture,  explained  the  cause 
and  illustrated  the  pressure  of  the  air,  we  proceed  in  the 
next  place  to  determine  its  actual  amount. 

JV*r-24-  There  are  many  ways  in 

gjjjjJH^  which  this  may  be  done.    The 

jjT  following  is  simple  :   Take  a 

,s~^&= — •  — .  pair   of   Magdeburg   hemis- 

pheres, the  area  of  the  sec- 
tion of  which  has  been  pre- 
viously determined  in  square 
inches;  exhaust  them  as  per- 
fectly as  possible  at  the  pump; 
and  then,  fastening  the  lower 
handle,  a,  to  a  firm  support, 
hang  the  other,  I,  Fig.  24,  to  the  hook  of  a  steelyard, 
and  move  the  weight  until  the  hemispheres  are  pulled 
apart.  It  will  be  found  that  this  commonly  takes  place 
when  the  weight  is  sufficient  to  overcame  a  pressure  of 
fifteen  pounds  on  every  square  inch. 

This  may  serve  as  an  elementary  illustration,  but  there 
are  other  methods  much  more  exact.  Thus,  by  the  ba- 
rometer itself  we  may  determine  the  value  of  the  pressure 
with  precision.  If  we  had  a  barometer  which  was  ex- 
actly one  square  inch  in  section,  and  weighed  the  quanti- 
ty  of  mercury  it  contained  at  any  given  time,  it  would 

What  may  the  Magdeburg  hemisphere  be  made  to  prove?  How  may 
±  =  b£!  Prr,ed  by  the  barometer  ?  What  is  *e  pressure  of  the  air  on 


PRESSURE    OF    THE   AIR. 


27 


give  us  the  value  of  the  atmospheric  pressure  on  one 
square  inch,  because  the  weight  of  the  mercury  is  equal 
to  the  pressure  of  the  air.  And  by  calculation  we  can,  in 
like  manner,  obtain  it  from  tubes  of  any  diameter. 

The  phenomena  of  the  barometer  teach  us  that  this 
pressure  is  not  always  the  same,  but  it  undergoes  varia- 
tions. It  is  commonly  estimated  at  fifteen  pounds  on  the 
square  inch. 

There  are  two  other  ways  in  which  the  value  of  the 
pressure  of  the  air  is  stated.  It  is  equal  to  a  column  of 
mercury  thirty  inches  in  length,  or  to  a  column  of  water 
thirty-four  feet  in  length. 

We  are  now  able  to  understand  the  reason  of  the  great 
effects  to  which  the  pressure  of  the  air  may  give  rise.  In 
most  instances  these  effects  are  neutralized  by  counter- 
vailing pressures.  Thus,  the  body  of  a  man  of  ordinary 
size  has  a  surface  of  about  two  thousand  square  inches, 
the  pressure  upon  which  is  equal  to  thirty  thousand  pounds. 
But  this  amazing  force  is  entirely  neutralized,  because, 
as  we  have  seen,  the  atmospheric  pressure  is  equal  in  all 
directions,  upward,  downward,  and  laterally.  All  the 
cavities  and  the  pores  of  the  body  are  filled 
with  air,  which  presses  with  an  equal  force. 

The  following  experiments  may  further 
illustrate  the  general  principle  of  atmospher- 
ic pressure  : 

On  a  small,  flat  plate,  a,  Fig.  25,  furnished 
with  a  stop-cock,  b,  which  terminates  in  a 
narrow  pipe,  c,  let  there  be  placed  a  tall  re- 
ceiver from  which  the  air  is  to  be  exhausted 
by  the  pump.  The  stop-cock  b  being  clo- 
sed, and  the  instrument  being  removed  from 
the  pump,  b  is  to  be  opened,  while  the  lower 
portion  of  its  tube  dips  into  a  bowl  of  water. 
Under  these  circumstances  the  water  is 
pressed  up  in  a  jet  through  c,  and  forms  a 
fountain  in  vacuo. 

On  the  top  of  a  receiver,  Fig.  26,  let 
there  be  cemented,  air-tight,  a  cup  of  wood, 

What  is  the  length  of  an  equivalent  column  of  mercury  ?  What  is  it  in 
the  case  of  water?  What  amount  of  pressure  is  there  on  the  body  of  a 
man  ?  By  what  is  this  counteracted  ?  Describe  the  fountain  in  vacuo. 
How  may  mercury  be  pressed  through  the  pores  of  wood  ? 


28 


ELASTICITY    OF    AIR. 


Fig.  26.  a,  terminating  in  a  cylindrical  piece,  b,  the 
pores  of  which  run  lengthwise.  Beneath  this 
let  there  be  placed  a  tall  jar,  c.  Now,  if  the 
wooden  cup  be  filled  with  quicksilver,  the  jar 
being  previously  placed  on  the  pump,  and  ex- 
haustion made,  the  metal  will  be  pressed 
through  the  pores  of  the  wood  and  descend 
in  a  silver  shower.  The  jar,  c,  should  be  so 
placed  as  to  prevent  any  of  the  quicksilver 
getting  into  the  interior  of  the  pump. 

There  are  many  substances  which  exist  in 
the  liquid  condition,  merely  because  of  the  press- 
ure of  the  air.  Take  a  glass  tube,  A,  Fig.  27, 
closed  at  one  end  and  open  at  the  other,  and 
having  filled  it  with  water,  invert  it  in  a  jar,  B ; 
introduce  into  it  now  a  little  sulphuric  ether, 
which  will  rise,  because  of  its  lightness,  to  the 
top  of  the  tube,  at  a.  Place  the  apparatus  be- 
neath the  receiver  of  the  air-pump,  arid  exhaust.  The 
ether  will  now  be  seen  to  abandon  the  liquid  and  assume 
the  gaseous  form,  filling  the  entire  tube  and  looking  like 
air.  On  allowing  the  pressure  again  to  take  effect,  it  again 
relapses  into  the  liquid  form. 

Fig.  28.         The  following  experiments  illustrate  the  elas- 
ticity of  the  air : 

Take  a  glass  bulb,  a,  Fig.  28,  which  has,  a 
tube,  b,  projecting  from  it,  the  open  extremity 
of  which  dips  beneath  some  water  in  a  cup,  c; 
the  tube  and  the  bulb  being  likewise  full  of 
water,  except  a  small  space  which  is  occupied 
by  a  bubble  of  air  at  a.  Invert  over  the  whole 
ajar,  d,  and,  placing  the  arrangement  on  the  pump,  ex- 
haust. It  will  be  found,  as  the  exhaustion  goes  on,  that 
the  bubble  a  steadily  increases  in  size  until  it  fills  all 
the  bulb,  and  even  the  tube.  On  readmitting  the  press- 
ure the  bubble  collapses  to  its  original  size.  The  air 
is,  therefore,  dilatable  and  condensible  —  that  is,  it  is 
elastic. 

If  a  bottle,  the  sides  of  which  are  square  and  the  mouth 
hermetically  closed,  be  placed  beneath  a  receiver,  and 

Why  does  sulphuric  ether  retain  the  liquid  state  ?    When  the  pressure 
what  becomes  of  the  ether?    What  does  experiment  Fig.  28 


THE    CONDENSER. 


29 


Fig.  29. 


the  pressure  removed,  tbe  air  imprisoned  in 
the  interior  exerting  its  elastic  force,  will  vio- 
lently burst  the  bottle  to  pieces.'  It  is,  there- 
fore, well  to  cover  it  with  a  wire  cage,  as  rep- 
resented in  Fig.  29. 

The  elastic  force  of  the  air  increases  with  its 
density.     Powerful  effects,  therefore,  arise  by 
condensing  air  into  a  limited  space.     The  con- 
denser, which  is  an  instrument  for  this  pur- 
pose, is  represented  in  Fig.  30.     It  consists 
of  a  tube,  a  b,  in  which  there  moves  by  a 
handle,  g,  a  piston^  In  one  side  of  the  tube, 
at  c,  there  is  an  aperture,  and  at  the  lower 
part,  d,  there  is  a  valve,  e,  opening  down- 
ward. On  pushing  the  piston  down,  the  airbe- 
iieathit  is  compressed,  and,  opening  the  valve 
e,  by  its  elastic  force,  accumulates  in  the  re- 
ceiver, R.     When  the  piston  is  pulled  up  a      ; 
vacuum  is  made  in  the  tube;  but  as  soon  as 
it  passes  the  aperture,  c,  the  air  rushes  in. 
Another  downward  movement  drives  this 
through  the   valve  into  the  receiver,   and 
the  process  may  be  continued  until  the  elas- 
tic force  of  the  included  air  becomes  very 
great. 

If  the  receiver  be  partly  filled  with  water, 
and  there  be  placed  in  it  a  piece  of  wax,  an  egg, 
or  any  yielding  or  brittle  bodies,  it  will  be  found 
impossible  to  alter  their  figure  by  condensing 
the  air  to  any  extent  whatever.  And  this  arises 
from  the  circumstance  already  explained — that 
the  pressure  generated  is  equal  in  all  direc- 
tions. 

The  Cartesian  image  is  a  grotesque  figure, 
made  of  glass,  Fig.  31,  hollow  within  and  filled 
with  water  to  the  height  c  d.  The  upper  part, 
a,  is  filled  with  air.  The  water  is  introduced  through  the 
tail,  6,  and  the  quantity  of  it  is  so  adjusted  that  the  figure 
just  floats  in  water.  If,  therefore,  it  be  placed  in  a  deep 

Under  what  circumstances  may  flat  bottles  be  broken  ?  What  relation 
is  there  between  elastic  force  and  density  ?  Describe  the  condenser.  Why 
are  not  brittle  bodies  broken  in  such  an  instrument  ?  What  is  the  reason 
of  the  motions  of  the  Cartesian  images  ? 


Fig.  31. 


30  MISCELLANEOUS     EXPERIMENTS. 

jar  quite  full  of  that  liquid,  and  a  cover  of  India-rubber 
Fig.  32.  or  bladder  tied  on,  as  seen  in  Fig.  32,  the  fig- 
ure floats  up  at  the  top ;  but  by  pressing  with 
the  finger  on  the  cover,  more  water  is  forced  into 
its  interior,  through  the  tail,  b,  and  it  descends 
to  the  bottom.  On  removing  the  finger  the  elastic 
force  of  the  air,  a,  drives  out  this  excess  of  wa- 
ter, and  the  image,  becoming  lighter,  reascends. 
If  the  tail  be  turned  on  one  side,  as  represent- 
ed, the  efflux  of  the  water  taking  effect  in  a  lat- 
eral direction,  the  figure  spins  round  in  its  move- 
ments and  performs  grotesque  evolutions. 

On  precisely  the  same  principle,  if  a  small 
k]a(jder,  only  partly  full  of  air,  be  sunk  by  a 
weight,  Fig.  33,  to  the  bottom  of  a  deep  glass 
of  water,  on  covering  the  whole  with  a  re- 
ceiver and  exhausting,  the  elastic  force  of  the 
included  air  dilates  the  bladder,  which  rises 
to  the  top,  carrying  with  it  the  weight. 
When  the  pressure  is  readmitted  the  blad- 
der collapses  and  descends  again  to  the  bot- 
tom of  the  jar. 
There  are  numerous  machines  in  which  the  elastic  force 
of  air  is  brought  into  operation,  such  as  the  air-gun, 
blowing  machines,  &c.  Indeed,  the  various  applications 
of  gunpowder  itself  depend  on  this  principle — that  ma- 
terial on  ignition  suddenly  giving  rise  to  the  evolution  of 
an  immense  quantity  of  gas,  which  exerts  a  great  elastic 
force. 

What  is  the  cause  of  the  ascent  and  descent  of  the  little  bladder,  Fig. 
33  ?    On  what  do  the  air-gun  and  the  action  of  gunpowder  depend  1 


MARRIOTTE'S  LAW  31 


LECTURE  VII. 

PROPERTIES  OF  THE  AIR. — Marriotte's  Law. — Proof  for 
Compressions  and  Dilatations. —  Case  in  which  it  Fails. 
— Resistance  of  the  Air  to  Motion. —  The  Parachute. — 
The  Air  transmits  Sound;  supports  Animal  Life,  Com- 
bustion, and  Ignition. — Exists  in  the  pores  of  some  Bodies 
and  is  dissolved  in  others. 

ATMOSPHERIC  air  being  thus  a  highly  compressible  and 
expansible  substance,  we  have  next  to  inquire  what  is 
the  amount  of  its  compressibility  under  different  degrees 
of  force  ]  This  has  been  determined  experimentally  by 
different  philosophers,  the  true  law  having  first  been  dis- 
covered by  Boyle  and  Marriotte. 

The  density  and  elasticity  of  air  are  directly  as  the  force 
of  compression. 

The  volume  whicJi  air  occupies  is  inversely  as  the  press- 
ure  upon  it. 

To  illustrate,  and  at  the  same  time  to  prove  these  laws, 
we  make  use  of  a  tube,  a  d  c  b,  so'  bent  that  it  has  Fitr-  34. 
two  parallel  branches,  a  and  b.  It  is  closed  at  b, 
and  has  a  funnel-mouth  at  a.  Sufficient  mercury  is 
poured  into  the  tube  to  close  the  bend  and  to  insu- 
late a  volume  of  air  in  b  d.  Of  course  this  air  ex- 
ists under  a  pressure  of  one  atmosphere  equal  to  a 
column  of  mercury  thirty  inches  long.  Through  the 
funnel,  a,  mercury  is  now  to  be  poured  ;  as  it  accu- 
mulates it  presses  upon  the  air  in  d  b,  and  re- 
duces its  volume  to  c.  If,  in  this  manner,  a  column 
thirty  inches  long  be  introduced,  it  will  be  found  that  the 
air  in  b  d  is  reduced  to  half.  There  are,  therefore,  now 
two  atmospheres  pressing  on  the  included  air — the  atmos- 
phere itself  being  one,  and  the  thirty  inches  of  mercury 
the  other.  Two  atmospheres,  therefore,  reduce  a  given 
quantity  of  air  into  half  its  volume. 

In  the  same  manner  it  could  be  proved,  if  the  tube 


What  is  Marriotte's  laXv  ?  Describe  Marriotte's  instrument.  What  is 
its  use  ?  When  the  pressure  on  a  gas  is  doubled,  tripled,  quadrupled,  what 
Aolume  does  it  assume  ? 


RESISTANCE    OF   AIR. 


Fig.  35. 
Id 


were  long  enough,  that  the  introduction  of  another  thirty 
inches  of  mercury,  giving  a  pressure  of  three  atmospheres, 
would  condense  the  air  to  one-third,  that  four  would  com- 
press it  to  one-fourth,  five  to  one-fifth,  &c. 

The  truth  of  this  law  may  be  proved  for  rare- 
factions as  well  as  condensations.  For  this 
purpose  let  there  be  taken  a  long  tube,  a  b, 
Fig.  35,  open  at  the  end,  b,  and  closed  at  a, 
with  a  screw ;  a  jar,  A,  filled  with  mercury  to  a 
sufficient  height,  is  also  to  be  provided.  Now 
let  the  screw  at  a  be  opened  and  the  tube. de- 
pressed in  the  mercury  until  the  metal,  by 
rising,  leaves  in  the  tube  a  few  inches  of  air. 
The  screw  is  now  to  be  closed  and  the  tube  lift- 
ed. The  included  air  at  once  dilates  and  a  col- 
umn  of  mercury  is  suspended.  It  will  be  found 
that  when  the  air  has  dilated  to  double  its  vol- 
ume, the  length  of  the  mercurial  column  in  the 
tube  will  be  fifteen  inches — that  is,  half  the  ba- 
rometric length. 

*  By  such  experiments,  it  therefore  appears  that 
Marriotte's-  law  holds  both  for  condensations  and  rarefac- 
tions. This  law  has  been  verified  until  the  air  has  been 
condensed  twenty-seven  times  and  rarefied  one  hundred 
and  twelve  times.  In  the  case  of  gases,  which  easily  as- 
sume the  liquid  form,  it  is,  however  departed  from  as  that 
point  is  approached. 

Besides  the  properties  already  de- 
scribed, atmospheric  air  possesses 
others  which  require  notice.  Among 
these  may  be  mentioned  its  resist- 
ance to  motion. 

This  property  may  be  exhibited 
by  means  of  the  two  wheels,  a  b,  Fig. 
36,  which  can  be  put  in  rapid  rota- 
tory motion  by  the  rack,  d,  which 
moves  up  and  down  through  an  air- 
tight stuffing-box,  e.  The  wheels 
are  so  arranged  that  the  vanes  of  a 
move  through  the  air  edgewise,  but 

How  may  this  be  proved  for  rarefactions  ?  To  what  extent  has  this  law 
been  verified  ?  How  may  the  resistance  of  the  air  be  proved  ?  In  a  vacu- 
um is  there  any  resistance  ? 


Fig.  36. 


RESISTANCE    OP    AIR. 


33 


Fig.  37. 


those  of  b  with  their  broad  faces.  On  pushing  down  the 
rack,  d,  and  making  the  wheels  rotate  with  equal  rapid- 
ity in  the  atmospheric  air,  one  of  them,  a,  will  be  found 
to  continue  its  motion  much  longer  than  the  other,  b:  and 
that  this  arises  from  the  resistance  which  b  experiences 
from  the  air  is  proved  by  making  them  rotate  in  the 
receiver  from  which  the  air  has  been  exhausted,  when  b 
will  continue  its  motion  as  long  as  a,  both  ceasing  to  re- 
volve simultaneously. 

The  water-hammer  affords  another  instance  of  the  same 
principle.  It  consists  of  a  tube  a  foot  or  more  long  and 
half  an  inch  in  diameter.  In  it  there  is  included  a  small 
quantity  of  water,  but  no  atmospheric  air.  When  it  is 
turned  upside  down  the  water  drops  from  end  to  end,  and 
emits  a  ringing,  metallic  sound.  If  there  was  any  air  in 
the  tube,  it  would  resist  or  break  the  fall  of  the  water. 
A  well-made  mercurial  thermometer  exhibits  the  same 
fact.  If  there  is  a  perfect  vacuum  in  its  tube,  on  turning 
the  instrument  upside  down  the  metal  drops  like  a  hard, 
solid  body  against  the  closed  end. 

The  Parachute  is  a  machine 
by  which  aeronauts  may  de- 
scend from  a  balloon  to  the 
ground  in  safety.  It  bears  a 
general  resemblance  to  an 
umbrella,  and  consists  of  a 
strong  but  light  surface,  a  a, 
Fig.  37,  from  which  a  car, 
b,  is  suspended.  When  it 
is  detached  from  the  bal- 
loon, it  descends  at  first  with 
an  accelerated  velocity,  but 
this  is  soon  checked  by  the 
resistance  of  the  air,  and  the 

|  machine  then  falls  at  a  rate 

i  nearly  uniform,  and  very  mod- 

;  erate. 

In  virtue  of  its  elasticity,  atmospheric  air  is  the  common 

I  medium  for  the  transmission  of  sounds.     Under  the  receiv- 

\  er  of  an  air-pump  let  there  be  placed  a  bell,  a,  Fig.  38,  the 
hammer,  b,  of  which  can  be  moved  on  its  pivot,  c,  by  means 

Describe  the  parachute  and  its  mode  of  action.  How  may  it  be  proved 
that  atmospheric  air  transmits  sound  ? 


34 


AIR    SUPPORTS    LIFE. 


of  a  lever,  h,  which  is  worked  by  a  rod  passing  through 
Fig.  38  the  stuffing-box,  e.    The  bell  is  placed 

on  a  leather  drum,  g,  and  fastened 
down  to  the  pump-plate  by  means 
of  a  board,  d.  While  the  air  is  yet 
in  the  receiver,  the  sound  is  quite 
audible,  but  on  exhausting  it  becomes 
fainter  and  fainter,  and  at  last  can  no 
longer  be  heard.  On  readmitting  the 
air  the  sound  gradually  increases,  arid 
at  last  acquires  its  original  intensity. 
The  leather  cushion,^,  is  necessary  to 
prevent  the  transmission  of  the  sound 
through  the  solid  part  of  the  pump. 
The  air  also  is  absolutely  necessary  for  the  support  of 
Fig.  39.  life.  The  higher  warm-blooded  animals 

die  when  the  air  is  only  partially  rare- 
fied. A  rabbit,  or  other  small  animal, 
placed  under  an  air-pump  jar  may  re- 
main there  several  minutes  without  being 
much  disturbed ;  but  if  we  commence 
withdrawing  the  air  the  animal  instantly 
shows  signs  of  distress,  and  if  the  exper- 
iment is  continued,  soon  dies. 

So,  too,  if  a  jar  containing  some  small 
fishes  be  placed  under  an  exhausted  re- 
ceiver, the  animals  either  float  on  their 
backs  at  the  surface  of  the  water,  or 
descend  only  by  violent  muscular  exertions.  Fishes 
respire  the  air  which  is  dissolved  in  water,  and  hence 
it  is  somewhat  remarkable  that  they  continue  to  live 
for  a  considerable  length  of  time  in  an  exhausted  re- 
ceiver. 

The  air  is  also  necessary  to  all  processes  of  combustion. 
If  a  lighted  candle  be  placed  under  a  receiver,  it  will 
burn  for  a  length  of  time  ;  but  if  the  air  be  withdrawn 
by  the  pump,  it  presently  dies  out.  The  smoke  also 
descends  to  the  bottom  of  the  receiver,  there  being  no 
air  to  buoy  it  up. 

Why  is  it  necessary  that  the  bell  should  rest  on  a  cushion  ?  Prove  that 
air  is  necessary  for  the  support  of  life.  Do  fishes  die  at  once  in  an  ex- 
hausted receiver?  Prove  that  the  air  is  necessary  to  support  combus- 
tion. 


AIR   EXISTS    IN    PORES. 


35 


If  a  gun-lock  be  placed-  in  an  exhausted  receiver,  and 
the  flint  be  made  to  stiike,  no  sparks  pig.  40. 

whatever  appear ;  and,  consequently, 
if  there  were  powder  in  the  pan,  it 
could  not  be  exploded.  The  produc- 
tion of  sparks  by  the  flint  and  steel  is 
due  to  small  portions  of  the  latter  which 
are  struck  off  by  the  percussion  burn- 
ing in  the  air,  and  when  the  air  is  re- 
moved that  combustion  can,  of  course, 
no  longer  take  place. 

By  taking  advantage  of  the  expansi- 
bility of  the  air,  we  are  able  to  prove 
Fig.  41.  tnat  it  is  included  in  the  pores 
of  many  bodies.  Thus,  if  an 
egg  is  dropped  into  a  deep  jar 
of  water,  and  this  covered  with 
a  receiver  as  soon  as  exhaustion  is  made,  a  multi- 
tude of  air  bubbles  continually  ascend  through  the 
water.  Or  if  a  glass  of  porter  be  placed  beneath 
such  a  receiver,  its  surface  is  covered 
with  a  foam,  the  carbonic  acid  gas, 
which  is  the  cause  of  its  agreeable 
briskness,  escaping  away.  And  even  com- 
mon river  or  spring  water  treated  in  the  same 
manner  exhibits  the  escape  of  a  considerable 
quantity  of  gas,  which  ascends  through  it  in 
small  bubbles,  and  gives  it  a  sparkling  ap- 
pearance. 

Why  does  a  gun-lock  fail  to  give  sparks  in  vacuo  ?  How  may  the  pres- 
ence of  air  in  the  pores  of  bodies  be  proved  I  Does  water  contain  dis- 
solved air  ? 


36  LOSS    OF    WEIGHT    IN    AIR. 


LECTURE  VIII. 

PROPERTIES  OF  THE  AIR.— Loss  of  Weight  of  Bodies  in 
the  Air. —  Theory  of  Aerostation. —  The  Montgolfier 
Balloon. —  The  Hydrogen  Balloon. — Mode  of  Controll- 
ing Ascent  and  Descent. — Artificial  and  Natural  Cur- 
rents in  the  Air. —  Velocity  with  which  Air  flows  into  a 
Vacuum. —  Velocity  of  Efflux  of  different  Gases. — Prin- 
ciples of  Gaseous  Diffusion. —  These  Principles  regulate 
the  Constitution  of  the  Atmosphere. 

ON  principles  which  will  be  fully  explained  when  we 
come  to  speak  of  specific  gravity,  it  appears  that  a  solid 
immersed  in  a  fluid  loses  a  portion  of  its  weight.  It 
follows,  of  course,  that  a  substance  weighs  less  in  the  air 
than  it  does  in  vacuo. 

To  one  arm  of  a  balance,  a,  Fig.  43,  let  there  be.  hung 
Fig.  43.  a  light  glass  globe,  c,  coun- 

terpoised in  the  air  on  the 
other  arm,  b,  by  means  of  a 
weight.  If  the  apparatus  be 
placed  beneath  a  receiver, 
and  the  air  exhausted,  the 
H  globe  c,  descends,  but  on  re- 
admitting the  air  the  equi- 
librium is  again  restored. 
This  instrument  was  former- 
ly used  for  determining  the 
density  of  the  air. 
A  substance  that  has  the  same  density  as  atmospheric 
air,  when  it  is  immersed  in  that  medium,  loses  all  its 
weight,  and  will  remain  suspended  in  it  in  any  position 
in  which  it  may  be  placed.  But  if  it  be  lighter,  it  is 
pressed  upward  by  the  aerial  particles,  and  rises  upon 
the  same  principle  that  a  cork  ascends  from  the  bottom 
of  a  bucket  of  water.  And  as  the  density  of  the  air  con- 

What  difference  is  there  in  the  weight  of  a  body  in  the  air  and  in  vacuo  ? 
What  fact  is  illustrated  by  the  instrument,  Fig.  43  ?  Under  what  circum- 
stances does  a  substance  in  the  air  lose  all  its  weight  ?  On  what  principle 
do  air  balloons  depend  ? 


AIR    BALLOON.  37 

tinually  diminishes  as  we  go  upward,  it  is  evident  that 
such  a  body,  ascending  from  one  stratum  to  another,  will 
finally  attain  one  having  the  same  density  as  itself,  and 
there  it  will  remain  suspended. 

On  these  principles  aerostation  depends.  Air  balloons 
are  machines  which  ascend  through  the  atmosphere  and 
float  at. a  certain  altitude.  They  are  of  two  kinds:  1st, 
Montgolfier  or  rarefied  air  balloons ;  and,  2d,  Hydrogen 
gas  balloons. 

The  Montgolfier  balloon,  which  was  invented  by  the 
person  whose  name  it  bears,  consists  of  a  light  bag  of 
paper  or  cotton,  which  may  be  of  a 
spherical  or  other  shape ;  in  its  lower 
portion  there  is  an  aperture,  with  a 
basket  suspended  beneath  for  the  pur- 
pose of  containing  burning  material,  as 
straw  or  shavings.  On  a  small  scale,  a 
paper  globe  two  or  three  feet  in  diam- 
eter, with  a  piece  of  sponge  soaked  in 
spirits  of  wine,  answers  very  well.  The 
hot  air  arising  from  the  burning  matter 
enters  the  aperture,  distending  the  balloon,  and  makes  it 
specifically  lighter  than  the  air,  through  which,  of  course, 
it  will  rise. 

The  hydrogen  gas  balloon  consists,  in  like  manner,  of 
a  thin,  impervious  bag,  filled  either  with  hydrogen  or  com- 
mon coal  gas.  The  former,  as  usually  made,  is  from  ten 
to  thirteen  times  lighter  than  air ;  the  latter  is  somewhat 
heavier.  A  balloon  filled  with  either  of  these  possesses, 
therefore,  a  great  ascentional  power,  an%d  will  rise  to 
considerable  heights.  Thus,  Biot  and  Gay  Lussac,  in 
1804,  ascended  in  one  of  these  machines  to  an  elevation 
of  23,000  feet.  When  the  balloon  first  ascends,  it  ought 
not  to  be  full  of  gas,  for  as  it  reaches  regions  where  the 
pressure  is  diminished,  the  gas  within  it  is  dilated,  and 
though  flaccid  at  first,  it  will  become  completely  distended. 
If  it  were  full  at  the  time  it  left  the  ground,  there  would 
be  risk  of  its  bursting  open  as  it  arose.  The  gas  balloon 
requires  a  valve  placed  at  its  top,  so  that  gas  may  be 

How  many  kinds  of  them  are  there  ?  Describe  the  Montgolfier  balloon. 
Describe  the  hydrogen  balloon.  What  is  the  relative  weight  of  hydrogen 
and  air  ?  Why  must  not  the  machine  be  full  when  it  leaves  the  ground  ? 
How  is  it  made  to  ascend  and  descend  ? 


38  CURRENTS    IN    THE    AIR. 

discharged  at  pleasure,  and  the  machine  made  to  descend. 
The  aeronaut  has  control  over  its  motions  by  taking  up 
with  him  a  quantity  of  sand  in  bags,  as  ballast.  If  he 
throws  out  sand  the  balloon  rises,  and  if  Tie  opens  the 
valve  and  lets  the  gas  escape,  it  descends. 

The  rarefaction  which  air  undergoes  by  heat  makes  it, 
of  course,  specifically  lighter.  Warm  air,  therefore,  as- 
cends, and  cold  air  descends.  When  the  door  of  a  room 
which  is  very  warm  is  open,  the  hot  air  flows  out  at  the 
top,  and  the  cold  enters  at  the  floor:  these  currents  may 
be  easily  traced  by  holding  a  candle  near  the  bottom  and 
top  of  the  doOr.  In  the  former  position  the  flame  leans 
inward,  in  the  latter  it  is  turned  outward,  following  the 
course  of  the  draught. 

The  drawing  of  chimneys,  and  the  actipn  of  furnaces 
and  stoves  depends  on  similar  principles  :  the  column 
of  hot  air  contained  in  the  flue  ascending,  and  cold  air 
replacing  it  below. 

Similar  movements  take  place  in  the  open  atmosphere. 
When  the  sun  shines  on  the  ground  or  the  surface  of  the 
sea,  the  air  in  contact  becomes  warm,  and  rises  ;  it  is 
replaced  by  colder  portions,  and  a  continuous  current  is 
established.  The  direction  of  these  currents  is  changed 
by  a  variety  of  circumstances,  as  the  diurnal  rotation  of 
the  earth  and  other  causes  less  understood.  On  these 
depend  the  various  currents  known  as  Breezes,  Trade- 
winds,  Storms,  Hurricanes. 

The  atmosphere  does  not  rush  into  a  void  space  instan- 
taneously, but,  under  common  circumstances  of  density 
and  pressure,  jwith  a  velocity  of  about  1296  feet  in  one 
second.  Its  resisting  action  on  projectiles  moving  through 
it  with  great  velocities  is  intimately  connected  with  this 
fact.  A  cannon-ball,  moving  through  it  with  a  speed  of 
two  or  three  thousand  feet,  leaves  a  total  vacuum  behind 
it,  and  condenses  the  air  correspondingly  in  front.  It  is, 
therefore,  subjected  to  a  very  po-werful  pressure  continu- 
ally tending  to  retard  it.  The  rush  of  the  air  flowing 
into  the  vacuous  spaces  left  by  moving  bodies  is  the  cause 
'of  the  loud  explosions  they  make. 

How  does  increase  of  heat  affect  the  air?  How  may  the  currents  in  a 
warm  room  be  traced  ?  What  is  the  principle  on  which  furnaces  and  stoves 
depend  ?  How  do  winds  and  currents  in  the  air  arise  ?  What  is  the  rea- 
son that  a  cannon-ball  moving  in  the  air  has  its  velocity  rapidly  reduced  ? 


DIFFUSION    OF    GASES.  39 

When  gases  of  different  densities  flow  from  apertures 
of  the  same  size,  the  velocities  with  which  they  issue  are 
different,  and  are  inversely  as  the  square  roots  of  their 
densities.  The  lighter  a  gas  is  the  greater  is  its  issuing 
velocity ;  and  therefore  hydrogen,  which  is  the  lightest 
body,  moves,  under  such  circumstances,  with  the  greatest 
speed. 

The  experiment  represented  in  Fig.  45  illustrates 
these  principles.  Let  there  Fig.  45. 

be  a  tube,  a  b,  half  an  inch  , 

in  diameter  and  six  inches 
long,  the  end,  b,  being  open 
and  a  closed  with  a  plug 
of  plaster  of  Paris,  which 
is  to  be  completely  dried. 
Counterpoise  this  tube  on 
the  arm  of  a  balance,  and 
fill  it  with  hydrogen  gas, 
taking  care  to  keep  the 
plug  dry,  letting  the  open  end,  b,  of  the  tube  dip  just  be- 
neath the  surface  of  some  water  contained  in  a  jar,  C. 
In  a  very  short  time  it  will  be  discovered  that  the  hydro- 
gen is  escaping  through  the  plaster  of  Paris,  and  the  tube, 
filling  with  water,  begins  to  descend;  and  after  a  few  min- 
utes much  of  the  gas  will  have  gone  out,  and  its  place  be 
occupied  partly  by  atmospheric  air,  which  comes  in  in  the 
opposite  direction,  and  partly  by  the  water  which  has  risen 
in  the  tube. 

Even  when  gases  are  separated  from  each  other  by 
barriers,  which,  strictly  speaking,  are  not  porous,  the  same 
phenomenon  takes  place.  Thus,  if  with  the  finger  we 
spread  a  film  of  soap-water  over  the  mouth  of  a  bottle, 
«,  and  then  expose  it  under  a  jar  to  some  other  Fig.4f>. 
gas,  such  as  carbonic  acid,  this  gas  percolates  rap- 
idly through  the  film,  and,  accumulating  in  the  bot- 
tle, distends  the  film  into  a  bubble,  as  represented 
in  Fig.  46.  Meanwhile,  a  little  atmospheric  air  es- 
capes out  of  the  bottle  through  the  film  in  the  op- 
posite direction. 

What  is  the  law  under  which  gases  flow  out  of  apertures?  How  may 
it  be  proved  that  gases  can  percolate  through  porous  bodies,  such  as  plugs 
of  stucco?  How  may  it  be  proved  that  they  pass  through  films  of 
water  ^ 


40  DIFFUSION    OF    GASES. 

This  propensity  of  gases  to  diffuse  into  each  other  is 
clearly  shown  by  filling  a  bottle,  H,  Fig.  47, 
•with  a  very  light  gas,  as  hydrogen  ;  and  a  second 
one,  C,  with  a  heavy  gas,  as  carbonic  acid,  and 
putting  the  bottles  mouth  to  mouth.  Diffusion 
takes  place,  the  light  gas  descending  and  the 
heavy  one  rising  until  both  are  equally  com- 
mixed. We  see,  therefore,  that  this  property  of 
gases  is  intimately  concerned  in  determining  the 
constitution  of  the  atmosphere,  which  is  made 
up  of  different  substances,  some  of  which  are  light  and 
some  heavy — the  heavy  ones  not  sinking,  nor  the  light  ones 
ascending,  but  both  kept  equally  commixed  by  diffusion 
into  each  other. 

Do  the  same  phenomena  ensue  when  no  boundaries  or  harriers  inter- 
vene ?  What  have  these  principles  to  tlo  with  the  constitution  of  the  at- 
mosphere '! 


PROPERTIES    OF    LKJUID8.  41 


PROPERTIES  OF  LIQUIDS. 

HYDROSTATICS  AND  HYDRAULICS. 


LECTURE  IX. 

PROPERTIES  OP  LIQUIDS. — Extent  and  Depth  of  the  Sea. 
— Its  Influence  on  the  Land. — Production  of  Fresh  Wa- 
ters.— Relation  of  Liqiiids  and  Gases. — Physical  Con- 
dition of  Liquids. — Different  Degrees  of  Liquidity. — 
Florentine  Experiment  on  the  Compression  of  Water. — 
Oersted's  Experiments. —  Compressibility  of  other  Li- 
quids. 

HAVING  disposed  of  the  mechanical  properties  of  at- 
mospheric air,  which  is  the  type  of  gaseous  bodies,  in  the 
next  place  we  pass  to  the  properties  of  water,  which  is  the 
representative  of  the  class  of  Liquids. 

About  two  thirds  of  the  surface  of  the  earth  are  covered 
with  a  sheet  of  water,  constituting  the  sea,  the  average 
depth  of  which  is  commonly  estimated  at  about  two  miles. 
This,  referred  to  omr  usual  standards  of  comparison,  im- 
presses us  at  once  with  an  idea  of  the  great  amount  of 
water  investing  the  globe ;  and,  accordingly,  imaginative 
writers  continually  refer  to  the  ocean  as  an  emblem  of 
immensity. 

But,  referred  to  its  own  proper  standard  of  compari- 
son— the  mass  of  the  earth — it  is  presented  to  us  under  a 
very  different  aspect.  The  distance  from  the  surface  to 
the  center  of  the  earth  is  nearly  four  thousand  miles. 
The  depth  of  the  ocean  does  not,  therefore,  exceed  ?TVir 
part  of  this  extent :  and  astronomers  have  justly  stated, 
that  were  we  on  an  ordinary  artificial  globe  to  place  a 

What  are  the  estimated  dimensions  of  the  sea  ?  How  do  these  coin- 
pare  with  the  size  of  the  earth  itself? 


42  THE    SEA. 

representation  of  the  ocean,  it  would  scarcely  exceed  in 
thickness  the  film  of  varnish  already  placed  there  by  the 
manufacturer. 

In  this  respect  the  sea  constitutes  a  mere  aqueous  film 
on  the  face  of  the  globe.  Yet,  insignificant  as  it  is  in 
reality,  it  has  been  one  of  the  chief  causes  engaged  in 
shaping  the  external  surface,  and  also  of  modeling  the 
interior  to  a  certain  depth — for  geological  investigations 
have  proved  the  former  action  of  the  ocean  on  regions  now 
far  removed  from  its  influence,  in  the  interior  of  conti- 
nents ;  and  also  its  mechanical  agency  in  the  formation 
of  the  sedimentary  or  stratified  rocks  which  are  of  enor- 
mous superficial  extents  and  often  situated  at  great  depths. 

Besides  the  salt  waters  of  the  sea,  there  are  collections 
of  fresh  water,  irregularly  disposed,  constituting  the  dif- 
ferent lakes,  rivers,  &c.  The  direct  sources  of  these 
are  springs,  which  break  forth  from  the  ground,  the  little 
streams  from  which  coalesce  into  larger  ones.  But  the 
true  source  of  all  our  terrestrial  waters  is  the  sea  itself.  By 
the  shining  of  the  sun  upon  it  a  portion  is  evaporated  into 
the  air,  and  this,  carried  away  by  winds  and  condensed 
again  by  cold,  descends  from  the  atmosphere  as  showers 
of  rain,  which,  being  received  upon  the  ground,  perco- 
lates until  it  is  stopped  by  some  less  pervious  stratum, 
and  flowing  along  this  at  last  breaks  out  wherever  there 
is  opportunity  in  the  low  grounds — thus  constituting  a 
spring.  Such  streamlets  coalesce  into  rivers,  which  find 
their  way  back  again  to  the  sea,  the  point  from  which 
they  originally  came — an  eternal  round,  which  is  repeat- 
ed for  centuries  in  succession.  * 

From  these  more  obvious  phenomena  of  nature  we  dis- 
cover a  relationship  between  aerial  and  liquid  bodies — 
the  one  passing  without  difficulty  into  the  other  form — 
and,  indeed,  many  of  the  most  important  events  around 
us  depending  on  that  fact.  Experiment  also  shows  that, 
in  many  instances,  substances  which  under  all  common 
circumstances  exist  in  the  gaseous  condition,  can  be  made 
to  assume  the  liquid.  Thus,  carbonic  acid,  which  is  one 
of  the  constitutents  of  the  atmosphere,  can  by  pressure 
be  reduced  to  the  liquid  form,  and  can  even  be  made  to 

What  great  phenomena  have  arisen  from  the  action  of  the  sea  ?  To  what 
source  are  rivers  and  springs  due?  How  is  it  they  are  formed?  What  re 
lation  is  there  between  gases  and  liquids  ? 


DEGREES    OF    LldUIDITY.  43 

assume  that  of  a  solid.     The  main  agents  by  which  such 
transmutations  are  affected  are  cold  and  pressure. 

The  parts  of  liquids  seem  to  have  little  cohesion.  View- 
ing the  forms  of  matter  as  being  determined  by  the  rela- 
tion of  those  attractive  and  repulsive  forces  which  are 
known  to  exist  among  particles,  it  is  believed  in  that^ 
now  under  consideration — the  liquid — that  these  forces 
are  in  equilibrio.  For  this  reason,  therefore,  the  parti- 
cles of  such  bodies  move  freely  among  one  another;  and 
liquids,  of  themselves,  cannot  assume  any  determinate 
shape,  but  conform  their  figure  to  the  vessels  in  which 
they  are  placed.  Portions  of  the  same  liquid  added  to 
one  another  readily  unite. 

Among  liquids  we  meet  with  what  may  be  termed  dif- 
ferent degrees  of  liquidity.  Thus  the  liquidity  of  molasses, 
oil,  and  water,  is  of  different  degrees.  It  seems  as  though 
there  was  a  gradual  passage  from  the  solid  to  this  state, 
a  passage  often  exhibited  by  some  of  the  most  limpid 
substances.  Thus  alcohol,  when  submitted  to  an  extreme 
degree  of  cold,  assumes  that  partial  consistency  which  is 
seen  in  melting  beeswax,  yet  at  common  temperatures  it 
is  one  of  the  most  mobile  bodies  known.  So,  too,  that 
compound  of  tin  and  lead  which  is  used  by  plumbers  as  a 
solder,  though  perfectly  fluid  at  a  certain  heat,  passes,  in 
the  act  of  cooling,  through  various  successive  stages,  and 
at  a  particular  point  becomes  plastic  and  may  be  molded 
with  a  cloth. 

If  a  quantity  of  atmospheric  air  is  pressed  upon  by  any 
suitable  contrivance,  it  shrinks  at  once  in  volume.  We 
rhave  already  proved  this  phenomenon  and  determined  its 
laws.  If  water  is  submitted  to  the  same  trial,  the  result 
is  very  different — it  refuses  to  yield  :  for  this  reason,  inas- 
much as  the  same  fact  applies  to  the  whole  class,  liquids 
are  spoken  of  as  incompressible  bodies. 

It  was  at  one  time  thought  that  the  experiment  of  the 
Florentine  academicians,  who  filled  a  gold  globe  with 
water,  and  on  compressing  it  with  a  screw  found  the  wa- 
ter ooze  through  the  pores  of  the  gold,  proved  completely 
the  incompressibility  of  that  liquid.  But  more  recent  ex- 
Do  the  parts  of  liquids  cohere  ?  What  is  the  relation  between  their  at- 
tractive and  repulsive  forces  ?  Mention  some  of  the  distinctive  qualities 
ol  liquids.  Give  examples  of  different  degrees  of  liquidity.  What  exper- 
iment has  been  supposed  to  prove  that  water  is  incompressible  ? 


44 


COMPRESSIBILITY  OF    LIQJJIDS. 


periments  have  shown,  beyond  all  doubt,  that  liquids  are 
compressible,  though  in  a  less  degree  than  gases.  Thus, 
it  is  a  common  experiment  to  lower  a  glass  bottle,  filled 
with  water  and  carefully  stopped  with  a  cork,  into  the  sea. 
Fig.  48.  On  raising  it  again  the  cork  is  often  found  forced 
in,  and  the  water  is  uniformly  brackish.  But  in 
a  more  exact  manner  the  fact  can  be  proved, 
and  even  the  amount  of  compressibility  meas- 
ured, by  QErsted's'machine.  This  consists  of  a 
strong  glass  cylinder,  a  a,  Fig.  48,  filled  with 
water,  upon  which  pressure  can  be  exerted  by 
a  piston  driven  by  a  screw,  b.  When  the  screw 
is  turned  and  pressure  on  the  liquid  exerted,  it 
contracts  into  less  dimensions,  but  at  the  same 
time  the  glass,  a  a,  yielding,  distends,  and  the 
contraction  of  the  water  becomes  complicated 
with  the  expansion  of  the  glass  in  which  it  is 
placed. 

To  enable  us  to  get  7%id  of  this  difficulty,  the  instru- 
?49.  ment,  Fig.  49,  is  immersed  in  the  cylinder  of 
water,  as  seen  at  Fig.  48.  This  consists  of  a 
glass  reservoir,  e,  prolonged  into  a  fine  tube,  e  ft 
with  a  scale,  x,  attached  to  it.  The  reservoir  and 
part  of  the  tube  are  filled  with  water,  and  a  little 
column  of  quicksilver,  x,  is  upon  the  top  of  the  wa- 
ter, serving  to  show  its  position.  On  one  side  there 
is  a  gage,  d,  partially  filled  with  air.  It  serves  to 
measure  the  pressure. 

Now  when  the  instrument,  Fig.  49,  is  put  in  the 
cylinder  in  the  position  indicated  in  Fig.  48,  and 
pressure  made  by  the  screw,  b,  it  is  clear  that  the 
water  in  the  reservoir  will  be  compressed,  and  the 
glass  which  contains  it  being  pressed  upon  equally, 
internally  and  externally,  will  yield  but  very  little.  Mak- 
ing allowance,  therefore,  for  the  small  amount  of  com- 
pression which  the  glass  thus  equally  pressed  upon  un- 
dergoes, we  may  determine  the  compressibility  of  the 
water  as  the  force  upon  it  varies.  It  thus  appears  that 
water  diminishes  ^i^  Part  of  its  volume  for  each  at- 
mosphere of  pressure  upon  it.  In  the  same  way  the  com- 
pressibility of  alcohol  has  been  determined  to  be  TT£o^. 

Mention  some  that  prove  the  contrary.     Describe  (Ersted's  machine. 
What  is  the  amount  of  the  compressibility  of  water  ? 


HYDROSTATIC    PRESSURE.  45 


LECTURE  X. 

THE  PRESSURES  OP  LIQUIDS. — Divisions  of  Hydrodynam- 
ics.— Liquids  seek  their  own  Level. — Equality  of  press- 
ures.— Case  of  different  Liquids  pressing  against  each 
other. — General  Law  of  Hydrostatics. — Hydrostatic  Par- 
adox.— Law  for  Lateral  Pressures. — Instantaneous  com- 
munication of  Pressure. — Bramah's  Hydraulic  Press. 

To  the  science  which  describes  the  mechanical  proper- 
ties of  liquids  the  title  of  HYDRODYNAMICS  is  applied.  It 
is  divided  into  two  branches,  Hydrostatics  and  Hydraul- 
ics. The  former  considers  the  weight  and  pressure  of 
liquids,  the  latter  their  motions  in  canals,  pipes,  &c. 

A  liquid  mass  exposed  without  any  confinement  to  the 
action  of  gravity  would  spread  itself  into  one  continuous 
superficies,  for  all  its  parts  gravitate  independently  of  one 
another,  each  part  pressing  equally  on  all  those  around  it, 
and  being  pressed  on  equally  by  them. 

A  liquid  confined  in  a  receptacle  or  vessel  of  any  kind 
conforms  itself  to  the  solid  walls  by  which  it  is  surround- 
ed, and  its  upper  surface  is  perfectly  plane,  no  part 
being  higher  than  another.  This  level  of  surface  takes 
place  even  when  different  vessels  communicating  with 
each  other  are  used.  Thus,  if  into  a  glass  of  water  we 
dip  a  tube,  the  upper  orifice  of  which  is  temporarily 
closed  by  the  finger,  but  little  water  will  enter,  owing  to 
the  impenetrability  of  the  air ;  but,  as  soon  as  the  finger 
is  removed,  the  liquid  instantly  rises,  and  finally  settles  at 
the  same  level  inside  of  the  tube  that  it  occupies  in  the 
glass  on  the  outside. 

This  result  obviously  depends  on  the  equality  of  press- 
ure just  referred  to,  and  it  is  perfectly  independent  of 
the  form  or  nature  of  the  vessel.  If  we  take  a  tube  bent 

Into  what  branches  is  Hydrodynamics  divided  ?  Under  the  action  of 
gravity  what  form  does  a  free  liquid  assume  ?  What  is  the  effect  when  it 
is  inclosed  in  a  vessel  ?  Give  an  illustration  of  the  equality  of  pressure. 


46 


PRESSURE    OF    DIFFERENT    LIQUIDS. 


fig.  50. 


in  the  form  of  the  letter  U,  and  closing  one  of  its  branches 
with  the  finger,  pour  water  into  the  other,  as  soon  as  the 
finger  is  removed  the  liquid  rises  in  the  empty  branch, 
and,  after  a  few  oscillatory  movements,  stands  at  the  same 
level  in  both. 

If  one  of  the  branches  of  such  a  tube  is  much  wider 
than  the  other,  the  same    result  still  ensues. 
Thus,  as  in  Fig.  50,  we  might  have  a  reser- 
c    voir,  A  I,  exposing  an  area  of  ten,  or  a  huri- 
>    dred,  or  ten  thousand  times   that  of  a  tube 
rising  from  it,  B  G  C  H,  but  in  the  latter  a  liquid 
would  rise  no  higher  than  in  the  former,  both 
being  at  precisely  the  same  level,  A  D.     We 
perceive,  therefore,  from  such  an  experiment, 
,    that  the  pressure  of  liquids  does  not  depend 
on  their  absolute  weight,  but  on  their  vertical 
altitude.     The  great  mass  of  liquid  contained 
in  A  exerts  no  more  pressure  on  C  than  would 
a  smaller  mass  contained  in  a  tube  of  the  same 
dimensions  as  C  itself. 

j-  A  variation  of  this  experiment  will  throw 
much  light  upon  the  subject.  Instead  of  using 
one,  let  there  be  two  liquids,  of  which  the  spe- 
cific gravities  are  different.  Put  one  in  one  of 
the  branches  of  the  tube,aZ»c,  Fig.  51,  and  the 
i4  other  in  the  other.  Let  the  liquids  be  quicksil- 
13  ver  and  water.  It  will  be  found,  under  these 
circumstances,  that  the  water  does  not  press 
the  quicksilver  up  to  its  own  level,  but  that, 
for  every  thirteen  and  a  half  inches  vertical 
height  that  it  has  in  one  of  the  branches  the 
quicksilver  has  one  inch  in  the  other.  Of 
course,  as  they  communicate  through  the  hori- 
zontal branch,  Z>,  the  quicksilver  must  press 
against  the  water  as  strongly  as  the  water 
presses  against  it;  if  it  did  not,  movement  would  ensue. 
And  such  experiments,  therefore,  prove  that  it  is  the  prin- 
ciple of  equality  of  pressures  which  determines  liquids  to 
seek  their  own  level. 

From  this  it  therefore  appears  that  a  liquid  in  a  vessel 

Does  this  depend  on  the  mass  of  a  liquid  ?  Prove  that  it  depends  on  its 
height.  What  takes  place  when  liquids  of  different  densities  are  used  ? 
In  what  directions  do  liquids  press  ? 


51. 


HYDROSTATIC    PRESSURES. 


47 


Fig.  52. 


not  only  exerts  a  pressure  upon  the  bottom  in  the  di- 
rection in  which  gravity  acts,  but  also  laterally  and  up- 
ward. 

From  what  was  proved  by  the  experiment  represented  in 
Fig.  50,  it  follows  that  these  pressures  are  by  no  means  ne- 
cessarily as  the  mass,  but  in  proportion  to  the  vertical  height. 
If  one  hundred  drops  of  water  be  arranged  in  a  vertical  line, 
the  lowest  one  will  exert  on  the  surface  on  which  it  rests 
a  pressure  equal  to  the  weight  of  the  whole.  And  from 
such  considerations  we  deduce  the  general  rule  for  esti- 
mating the  pressure  a  liquid  exerts  upon  the  base  of  a 
vessel.  "  Multiply  the  height  of  the  fluid  by  the  area  of 
the  base  on  which  it  rests,  and  the  product  gives  a  mass 
which  presses  with  the  same  weight." 

Thus  in  a  conical  vessel,  E  C 
D  F,^.  52,  the  base,CD,  sus- 
tains a  pressure  measured  by 
the  column  A  B  C  D.  For  all 
the  rest  of  the  liquid  on.ly 
presses  on  ABCD  laterally, 
and  resting  on  the  sides  EC 
and  F  D,  cannot  contribute 
any  thing  to  the  pressure  on 
the  base,  C  D 

But  in  a  conical  vessel,  EC 
D  F,  Fig.  53,  the  pressure  on 
A  B  is  measured  by  A  B  C  D, 
as  before  ;  but  the  other  por- 
tions of  the  liquid,  not  rest- 
ing upon  the  sides,  press 
also  upon  the  bottom,  E  F, 
and  the  retult,  therefore,  is 
the  same  as  if  the  vessel 
were  filled  throughout  to  the 
height  C  A. 

This  law  is  nothing  more  than  an  expression  of  the  fact 
that  the  actual  pressure  of  a  liquid  is  dependent  on  its 
vertical  height  and  the  area  of  its  base.  Its  applications 
give  rise  to  some  singular  results.  Thus,  the  Hydro- 
static bellows  consists  of  a  pair  of  boards,  A,  Fig.  54, 


Fig.  53. 


Give  the  rule  for  finding  the  pressure  of  a  liquid  01 
sel  containing  it.    Describe  the  hydrostatic  bellows. 


on  the  base  of  the  ves- 


48 


HYDROSTATIC    PARADOX. 


united  together  by  leather,  and  from  the 
>e  lower  one  there  rises  a  tube,  e  B  e,  ending 
in  a  funnel-shaped  termination,  e.  If  heavy 
weights,  bed,  are  put  upon  the  upper 
board,  or  a  man  stands  upon  it,  by  pour- 
ing water  down  the  tube  the  weight  can 
be  raised.  It  is  immaterial  how  slender 
the  tube,  and,  therefore,  how  small  the 
quantity  of  water  it  contains,  the  total 
pressure  resulting  depends  on  the  area  of 
the  bellows-boards,  multiplied  by  the  ver- 
tical height  of  the  tube. 

Theoretically,  therefore,  it  appears  that 
a  quantity  of  water,  however  small,  can 
be  made  to  lift  a  weight  however  great — a  principle 
sometimes  spoken  of  as  the  HYDROSTATIC  PARADOX, 

But  liquids  exert  a  pressure  against  the  sides  as  well  as 
upon  the  bases  of  the  containing  vessel — the  force  of  that 
pressure  depending  on  the  height.  The  law  for  estima- 
ting such  pressure  is,  "  The  horizontal  force  exerted 
against  all  the  sides  of  a  vessel  is  found  by  multiplying 
the  sum  of  the  areas  of  all  the  sides  into  a  height  equal  to 
half  that  at  which  the  liquid  stands." 

When  bodies  are  sunk  in  a  liquid,  the  liquid  exerts  a 
pressure  which  depends  conjointly  on  the  surface  of  the 
solid  and  the  depth  to  which  its  center  is  sunk.  Thus,  if 
into  a  deep  vessel  of  water  we  plunge  a  bladder,  to  the 
neck  of  which  a  tube  is  tied,  the  bladder  and  part  of  the 
tube  being  filled  with  colored  water,  it  will  be  seen,  as  the 
bladder  is  sunk,  that  the  colored  water  rises  in  the  tube. 
A  pressure  exerted  against  one  portion  of  a  liquid  is 
instantly  communicated  throughout  the  whol&mass,  each 
particle  transmitting  the  same  pressure  to  those  around. 
A  striking  illustration  of  this  is  seen  when  a  Prince  Ru- 
pert's drop  is  broken  in  a  glass  of  water,  the  glass  being 
instantly  burst  to  pieces. 

Bramah's  press,  or  the  Hydrostatic  press,  is  an  illus- 
tration of  the  principle  developed  in  this  lecture — that 
every  particle  of  a  fluid  transmits  the  pressure  it  receives, 
in  all  directions,  to  those  around.  It  consists  of  a  small 

What  is  meant  by  the  hydrostatic  paradox  ?  Give  the  rule  for  finding 
lateral  pressures.  Prove  that  a  liquid  exerts  a  pressure  on  bodies  plunged 
in  it.  Give  an  illustration  of  the  instantaneous  communication  of  pressure. 


THE    HYDRAULIC    PRESS. 


49 


Fig.  55. 


metallic  forcing-pump,  a,  Fig.  55,  in  which  a  piston,  s,  is 
worked  by  a  lever,  c  b  d.  This  little  pump  communicates 
with  a  strong  cyl- 
indrical reser- 
voir, A,  in  which 
a  water-tight  pis- 
ton, S,  moves, 
having  a  stout 
flat  head,  P,  be- 
tween which  and 
a  similar  plate, 
R,  supported  in 
a  frame,  the  sub- 
stance to  be  com- 
pressed, W,  is 
placed.  The  cyl- 
inder, A, and  the 
forcing-pump,  with  the  tube  communicating  between  them, 
are  filled  with  water,  the  quantity  of  which  can  be  in- 
creased by  working  the  lever,  d.  Now  it  is  obvious  that 
any  force,  impressed  upon  the  surface  of  the  water  in  the 
small  tube,  a,  will,  upon  the  principles  just  described, 
be  transmitted  to  that  in  A,  and  the  piston,  S,  will  be 
pushed  up  with  a  force  which  is  proportional  to  its  area, 
compared  with  that  of  the  piston  of  the  little  cylinder,  a. 
If  its  area  is  one  thousand  times  that  of  the  little  one,  it 
will  rise  with  a  force  one  thousand  times  as  great  as  that 
with  which  the  little  one  descends — the  motive  force  ap- 
plied at  d,  moreover,  has  the  advantage  of  the  leverage 
in  proportion  as  c  d  is  greater  than  c  b.  On  these  princi- 
ples it  may  be  shown  that  a  man  can,  without  difficulty, 
exert  a  compressing  force  of  a  million  of  pounds  by  the 
aid  of  such  a  machine  of  comparatively  small  dimensions. 

Describe  the  hydraulic  press. 

c 


50  SPECIFIC    GRAVITY. 


LECTURE  XI. 

SPECIFIC  GRAVITY. — Definition  of  the  term. —  The  Stand- 
ards of  Comparison. — Method  for  Solids. — Case  when 
the  Body  is  Lighter  than  Water. — Method  for  Liquids 
by  the  Thousand-Grain  Bottle. — Effects  of  Temperature. 
— Standards  of  Temperature. — Other  Methods  for  Li- 
quids.— Method  for  Gases. — Effects  of  Temperature  and 
Pressure. —  The  Hydrometer  or  Areometer. 

BY  the  specific  gravity  of  bodies  we  mean  the  propor- 
tion subsisting  between  absolute  weights  of  the  same  vol- 
ume. Thus,  if  we  take  the  same  volume  of  water  and 
copper,  one  cubic  inch  of  each,  for  example,  we  shall  find 
that  the  copper  weighs  S'G  times  as  much  as  the  water: 
and  the  same  holds  good  for  any  other  quantity,  as  ten 
cubic  inches  or  one  cubic  foot.  When  of  the  same  vol- 
ume the  copper  is  always  S'6  times  the  weight  of  the 
water. 

Specific  gravity  is,  therefore,  a  relative  affair.  We  must 
have  some  substance  with  which  others  may  be  compared. 
The  standard ,  which  has  been  selected  for  solids  and 
liquids  is  water;  that  for  gases  and  vapors,  atmospheric 
air. 

When  we  speak  of  the  specific  gravity  of  a  substance 
which  is  of  the  liquid  or  solid  kind,  we  mean  to  express 
its  weight  compared  with  the  weight  of  an  equal  volume 
of  water.  Thus,  the  specific  gravity  of  mercury  is  13-5; 
that  is  to  say,  a  given  volume  of  it  would  weigh  13-5  times 
as  much  as  an  equal  volume  of  water. 

Apparently  the  simplest  way  for  the  determination  of 
specific  gravities  of  solids,  would  be  to  form  samples  of 
a  uniform  volume;  as,  for  instance,  one  cubic  inch. 
Their  absolute  weight,  as  determined  by  the  balance, 
would  be  their  specific  gravities. 

But  in  practice  so  many  difficulties  would  be  encoun- 
tered in  such  a  process  that  its  results  would  be  quite  in- 

What  is  meant  by  specific  gravity  ?  What  are  the  standards  of  com- 
parison? Describe  an  apparently  simple  method  of  determining  the  spe- 
cific gravity  of  solids. 


THOUSAND-GRAIN    BOTTLE.  51 

exact ;  and  the  principles  of  hydrostatics  furnish  us  with 
far  more  accurate  means  for  resolving  such  problems. 

To  determine  the  specific  gravity  of  a  solid  body,  it  is 
to  be  weighed  first  in  air  and  then  in  water.  In  the  latter 
instance  it  will  weigh  less  than  in  the  former,  because  it 
displaces  a  quantity  of  the  water  equal  to  its  own  volume, 
and  this  deficit  in  weight  is  the  weight  of  the  water  so 
displaced.  The  weight  in  air  and  the  loss  in  water  being 
thus  determined,  to  find  the  specific  gravity,  "  Divide  the 
weight  in  air  by  the  loss  in  water,  and  the  quotient  is  the 
specific  gravity." 

If  the  body  be  lighter  than  water,  there  must  be  affixed 
to  it  some  substance  sufficiently  heavy  to  sink  it,  the 
weight  of  which,  and  also  its  loss  of  weight  in  water  are 
previously  known.  Deduct  this  weight  from  the  loss  of 
the  bodies  when  immersed  together,  and  divide  the  abso- 
lute weight  of  the  light  body  by  the  remainder ;  the  quo- 
tient gives  the  specific  gravity. 

For  the  determination  of  the  specific  gravity  of  liquids 
several  methods  may  be  resorted  to. 
One  of  the  most  simple  is  by  the  Thou- 
sand-grain Bottle.  This  consists  of  a 
light  glass  flask,  <2,  Fig.  56,  the  stopper 
of  which  is  also  of  glass  with  a  fine  per- 
foration, b,  through  it.  When  the  bot- 
tle is  filled  with  distilled  water,  and  the 
stopper  inserted  in  its  place,  any  excess 
of  liquid  is  forced  through  the  perfora- 
tion, and  the  bottle,  on  being  weighed, 
should  be  found  to  contain  one  thousand 
grains  of  the  liquid  exactly. 
If  any  other  liquid  be  in  like  manner  placed  in  this 
bottle,  by  merely  ascertaining  its  weight  we  at  once  de- 
termine its  specific  gravity.  Thus,  if  it  be  filled  with  oil 
of  vitrol  or  muriatic  acid,  it  will  be  found  to  hold  1845 
grains  of  the  former  and  1210  of  the  latter.  Those  num- 
bers, therefore,  represent  the  specific  gravities  of  the 
bodies  respectively. 

This  instrument  enables  us  to  illustrate,  in  a  very  satis- 
factory manner,  the  effect  of  temperature  on  specific  grav- 

Give  the  general  hydrostatic  method.  What  is  done  when  the  body  is 
lighter  than  water  ?  Give  the  method  in  the  case  of  liquids  by  the  Thou- 
sand-grain Bottle. 


STANDARDS    OF    TEMPERATURE. 


ity.  It  has  been  said  that  the  Thousand-grain  bottle  is  so 
called  from  its  containing  precisely  one  thousand  grains 
of  water ;  but  very  superficial  consideration  satisfies  us 
that  this  can  only  be  the  case  at  a  particular  temperature. 
Suppose  the  bottle  is  of  such  dimensions  that  at  60°  Fah- 
renheit it  contains  exactly  one  thousand  grains,  if  we  raise 
its  temperature  to  70°  Fahrenheit,  the  water  will  expand, 
or  if  we  lower  it  to  50°  Fahrenheit  it  will  contract  exact- 
ly as  if  it  were  a  liquid  in  a  thermometer.  It  is,  there- 
fore, very  clear  that  temperature  must  always  enter  into 
these  considerations,  and  that  before  we  can  express  the 
relation  of  weight  between  any  substance,  whether  solid 
or  liquid,  and  that  of  an  equal  volume  of  water,  we  must 
specify  at  what  particular  temperature  the  experiment 
was  made.  For  many  purposes  60°  Fahrenheit  is  select- 
ed, and  for  others  391°  Fahrenheit,  which  is  the  temper- 
ature of  the  maximum  density  of  water. 

There  is  a  second  method  by  which  the  specific  gravity 
of  fluids  may  be  known.  It  is  to  weigh  a  given  solid  (as 
a  mass  of  glass)  in  the  fluids  to  be  tried,  and  determine 
the  loss  of  weight  in  each  case.  Inasmuch  as  the  solid 
displaces  its  own  volume  of  the  different  liquids,  the  losses 
it  experiences  when  thus  weighed  will  be  proportional  to 
the  specific  gravities.  The  following  rule,  therefore,  ap- 
plies :  "  Divide  the  loss  of  weight  in  the  different  liquids 
by  the  loss  of  weight  in  water,  and  the  quotients  will  give 
the  specific  gravities  of  the  liquids  under  trial." 

For  the  determination  of 
the  specific  gravities  of  gases 
a  plan  analogous  in  principle 
to  that  of  the  Thousand-grain 
bottle  is  resorted  to.  A  light 
glass  flask,  g,  exhausted  of  air, 
is  attached  by  means  of  the 
stop-cocks,  e  d,  to  the  jar,  c, 
containing  the  gas  to  be  tried. 
This  gas  has  been  passed 
through  a  drying-tube,  a,  by 
means  of  a  bent  pipe,  b,  into 
the  jar,  c,  over  mercury.  On 

Describe  the  effects  of  temperature  on  specific  gravity.  Give  another 
method  for  determining  the  density  of  liquids.  How  is  that  of  gases  dis- 
covered ? 


Fig.  57. 


THE    HYDROMETER.  53 

opening  the  stop-cock  the  gas  flows  into  g,  and  its  weight 
may  then  be  determined  by  the  balance. 

From  the  greater  dilatation  of  ga§es  by  heat,  all  that 
has  been  just  said  in  relation  to  the  effect  of  temperature 
on  specific  gravity  applies  here  still  more  strongly.  It  is 
to  be  recollected  that  this  form  of  bodies  is  compared 
with  atmospheric  air  taken  as  the  standard. 

For  gases  another  disturbing  agency  beside  tempera- 
ture intervenes  —  it  is  pressure.  Atmospheric  pressure  is 
incessantly  varying,  and  the  densities  of  gases  vary  with 
it.  It  is  not  alone  the  thermometer,  but  also  the  Barom- 
eter which  must  be  consulted,  and  the  temperature  and 
pressure  both  specified.  Besides,  great  care  must  be  taken 
in  transferring  the  gas  from  the  jars  in  which  it  is  con- 
tained, that  it  is  not  subjected  to  any  accidental  pressures 
in  the  apparatus  itself,  and  that  the  flask  in  which  it  is 
weighed  is  not  touched  by  the  hands  or  submitted  to  any 
other  warming  or  cooling  influences. 

For  the  determination  of  the  densities  of  liquids  there 
is  still  another  method,  often  more  convenient  than  the 
former,  and  very  commonly  resorted  to,  it  is  by  the  aid 
of  instruments  which  pass  under  the  name  of  Hydrometers 
or  Areometers. 

The  principle  on  which  these  act  is,  that  when  a  body 
floats  upon  water,  the  quantity  of  fluid  displaced  is  equal 
in  volume  to  the  volume  of  the  part  of  the  body  immersed, 
and  in  weight  to  the  weight  of  the  whole  body. 

Thus,  a  piece  of  cork  floating  on  the  surface  of  quick- 
silver, water,  and  alcohol,  sinks  in  them  to  very  different 
depths  :  in  the  quicksilver  but  little,  in  the  water  more, 
and  in  the  alcohol  still  deeper;  but  in  every  instance  the 
weight  of  the  quantity  of  the  liquid  displaced  is  equal  to 
that  of  the  cork. 

It  is  plain,  therefore,  that  to  determine  the  specific 
gravity  of  a  liquid,  we  have  only  to  determine  the  depth 
to  which  a  floating  body  will  be  immersed  in  it.  The 
hydrometer  fulfills  these  conditions.  It  consists  of  a  cylin- 
drical cavity  of  glass,  A,  Fig.  58,  on  the  lower  part  of 
which  a  spherical  bulb,  B,  is  blown,  the  latter  being 
filled  with  a  suitable  quantity  of  small  shot  or  quicksil- 


What  disturbing  effects  are  encountered  in  the  case  of  gases  ?    On  what 
principle  is  the  hydrometer  constructed. 


THE    HYDROMETER. 


ver.  From  the  cylindrical  portion,  A,  a  tube,  C,  rises,  in 
the  interior  of  which  is  a  paper  scale  bearing  the  divisions. 
Fig.  58  The  whole  weight  of  the  instrument  is  such  that 
it  floats  in  the  liquid  to  be  tried,  and  if  that  liquid 
is  to  be  compared  with  water,  and  is  lighter  than 
water,  the  zero  of  the  divided  scale  is  toward  the 
lower  end  of  the  paper;  but  if  the  liquid  be 
heavier  than  water,  the  zero  is  toward  the  top  of 
the  scale.  Tables  are  usually  constructed  so 
that,  by  their  aid,  when  the  point  at  which  the 
hydrometer  floats  in  a  given  liquid  is  determined 
in  any  experiment,  the  specific  gravity  is  ex- 
pressed opposite  that  number  in  the  table. 

Of  these   scale-hydrometers  we  have  several 
different  kinds,  according  as  they  are  to  deter- 
mine different  liquids.     Among  them  may  be  mentioned 
Fig.  59.     Beaume's  hydrometer,  an   instrument  of  con- 
stant use  in  chemistry.     In  the  finer  kinds  of 
areometers   the   weighted    sphere,  B,  Fig.  58, 
forms    the    bulb    of    a    delicate    thermometer, 
the    stem    of  which    rises    into   the    cavity,  A. 
This  enables  us  to  determine  the  temperature 
of  the  liquid  at  the  same  time  with  its  specific 
gravity. 

Nicholson's  gravimeter  is  a  hydrometer 
which  enables  us  to  determine  the  density 
either  of  solids  or  liquids.  It  is  represented  at 
Fig.  59. 


Describe  the  hydrometer. 


HYDROSTATIC    PRESSURE. 


55 


LECTURE  XIL 

HYDROSTATIC  PRESSURES  AND  FORMATION  OF  FOUNT- 
AINS.—  Fundamental  Fact  of  Hydrostatics  —  holds 
also  for  Gases. — Illustrations  of  Upward  Pressure. — 
.  Determination  of  Specific  Gravities  of  Liquids  on  these 
Principles. —  Theory  of  Fountains. —  Cause  of  Natural 
Springs. — Artesian  Wells. 

THE  fundamental  fact  in  hydrostatics  thus  appears  to 
be,  that  as  each  atom  of  a  liquid  yields  to  the  influence 
of  gravity  without  being  restrained  by  any  cohesive  force, 
all  the  particles  of  such  a  mass  must  press  upon  those 
which  are  immediately  beneath  them,  and  therefore  the 
pressure  of  a  liquid  must  be  as  its  depth. 

The  same  fact  has  already  been  recognized  for  elastic 
fluids,  in  speaking  of  the  mechanical  properties  of  the 
earth's  atmosphere,  which,  for  this  veiy  reason,  and  also 
from  the  circumstance  that  it  is  a  highly  compressible 
body,  possesses  different  densities  at  different  heights. 
The  lower  regions  have  to  sustain  or  bear  up  the  weight 
of  all  above  them,  but  as  we  go  higher  and  higher  this 
weight  becomes  less  and  less,  until  at  the  surface  it  ceases 
to  exist  at  all. 

We  have  already  shown  from  the 
nature  of  a  fluid  such  pressures  are 
propagated  equally  in  all  directions,  up- 
ward and  laterally,  as  well  as  downward. 
This  important  principle  deserves,  how- 
ever, a  still  further  illustration  from  the 
consequences  we  have  now  to  draw  from 
it.  Let  a  tube  of  glass,  a  &,  Fig.  60,  have 
its  lower  end,  b,  closed  with  a  valve  slightly 
weighted  and  opening  upward,  the  end,  a, 
being  open.  On  holding  the  tube  in  a 
vertical  position,  the  valve  is  kept  shut  by 
its  own  weight.  But  if  we  depress  it  in 

What  is  the  fundamental  fact  in  hydrostatics  ?  Does  this  hold  for  elastic 
fluids?  Describe  the  illustration  represented  in  Fig.  GO.  How  may  it  be 
made  to  prove  the  downward  pressure  of  water  ? 


Fig.  60. 


56 


LIQUIDS    SEEK    THEIR    LEVEL. 


a  vessel  of  water,  as  soon  afif  a  certain  depth  is  reached 
the  upward  pressure  of  the  water  forces  the  valve,  and 
the  tube  begins  to  fill.  Still  further,  if  before  immersing 
the  tube  we  fill  it  to  the  height  of  a  few  inches  with 
water,  we  shall  find  that  it  must  now  be  depressed  to  a 
greater  depth  than  before,  because  the  downward  pressure 
of  the  included  water  tends  to  keep  the  valve  shut. 

From  the  same  principles  it  follows,  that  whenever  a 
liquid  has  freedom  of  motion,  it  will  tend  to  arrange 
itself  so  that  all  parts  of  its  surface  shall  be  equidistant 
fro  A  the  center  of  the  earth.  For  this  reason  the  surface 
of  water  in  basins  and  other  reservoir^  of  limited  extent 
is  always  in  a  horizontal  plane ;  but  when  those  surfaces 
are  of  greater  extent,  as  in  the  case  of  lakes  and  the  sea, 
they  necessarily  exhibit  a  rounded  form,  conforming  to  the 
figure  of  the  earth.  It  is  also  to  be  remembered  that,  when 
liquids  are  included  in  narrow  tubes,  the  phenomena  of  cap- 
illary attraction  disturb  both  their  level  and  surface-figure. 
Fig.  61.  All  liquids,  therefore,  tend  to 

find  their  own  level.     This  fact  is 
well  illustrated  by  the  instrument, 
fj  Fig.  61,  consisting  of  a  cylinder 
V    of  glass,  «,  connected  by  means  of 
a  horizontal  branch  with  the  tube, 

b,  which  moves  on  a  tight  joint  at, 

c.  By  this  joint,  b  can  be  set  par- 
allel to  «,  or  in  any  other  position. 
If  a  is  filled  with  wa- 
ter to  a  given  height, 

the  liquid  immediately 
flows  through  the  hori- 
zontal connecting  pipe,  and  rises  to  the  same 
height  in  b  that  it  occupies  in  a.  Nor  does  it 
matter  whether  b  be  parallel  to  «,  or  set  at 
any  inclined  position,  the  liquid  spontaneously 
adjusts  itself  to  an  equal  altitude. 

The  same  liquid  always  occupies  the  same 
level.  But  when  in  the  branches  of  a  tube 
we  have  liquids,  the  specific  gravities  of  which 
are  different,  then,  as  has  already  been  stated  in  Lecture 

.   What  is  the  surface-figure  of  liquids  ?    Describe  the  illustration  given 
51'  1S  the  laW  °f  different  Ii(luids  pressing  on  each  other  in 


Fig.  62. 
c 


FORMATION    OF    FOUNTAINS. 


57 


Fig.  63. 


X.,  they  rise  to  different  heights.  The  law  which  deter- 
mines this  is,  "The  heights  of  different  fluids  are  inversely 
as  their  specific  gravities''  If,  therefore,  in  one  of  the 
branches  of  a  tube,  a  b,  Fig.  62,  some  quicksilver  is 
poured  so  as  to  rise  to  a  height  of  one  inch,  it  will  require 
in  the  other  tube,  b  c,  a  column  of  water  13^  inches  long 
to  equilibrate  it,  because  the  specific  gravities  of  quick- 
silver and  water  are  as  13^  to  1. 

A  very  neat  instrument  for  illustrating 
these  facts  is  shown  in  Fig.  63.  It  consists 
of  two  long  glass  tubes,  a  b,  which  are  con- 
nected with  a  small  exhausting-syringe,  c, 
their  lower  ends  being  open  dip  into  the 
cups,  w  a,  in  which  the  liquids  whose  spe- 
cific gravities  are  to  be  tried  are  placed.  Let 
us  suppose  they  are  water  and  alcohol.  The 
syringe  produces  the  same  degree  of  partial 
exhaustion  in  both  the  tubes,  and  the  two  li- 
quids equally  pressed  up  by  the  atmospher- 
ic air,  begin  to  rise.  But  it  will  be  found 
that  the  alcohol  rises  much  higher  than  the 
water — to  a  height  which  is  inversely  pro- 
portional to  its  specific  gravity. 

When  in  the  instrument,  Fig.  61,  we  bend 
the  tube,  b,  upon  its  joint,  so  that  its  end  is 
below  the  water-level  in  a,  the  liquid  now  be- 
gins to  spout  out :  or  if,  instead  of  the  jointed 
tube,  we  have  a  short  tube,  C  e  D,  Fig.  64, 
proceeding  from  the  reservoir,  A  B,  the  wa- 
ter spouts  from  its  termination  and  forms  a 
fountain,  E  F,  which  rises  nearly  to  the  same 
height  as  the  water-level.  The  resistance  of 
the  air  and  the  descent  of  the  falling  drops 
shorten  the  altitude,  to  which  the  jet  rises  to 
a  certain  extent.  On  the  top  of  the  fountain 
a  cork  ball,  G,  may  be  s  spended  by  the  play- 
ing water. 

The  same  instrument  may  be  used  to  show 
the  equality  of  the  vertical  and  lateral  press- 


Fig.  64. 


uies  at  any  point.     For  let  the  tube,  D  E,  be  removed  so 

At  what  heights  will  quicksilver  and  water  stand  ?  Describe  the  instru- 
ment, Fig.  63.  What  fact  does  it  show  ?  Under  what  circumstances  does 
a  liquid  spout  1  How  may  a  fountain  be  formed  ? 


58 


FORMATION    OF    FOUNTAINS. 


as  to  leave  a  circular  aperture  at  e ;  also  let  C  be  a  plug 
closing  an  aperture  in  the  bottom  of  exactly  the  same  size 
as  e.  Now  if  the  reservoir,  A  B,  be  filled  to  the  height 
g,  and  kept  at  that  point  by  continually  pouring  in  water, 
and  the  quantities  of  liquid  flowing  out  through  the  lateral 
aperture,  e,  and  the  vertical  one,  C,  be  measured,  they 
will  be  found  precisely  the  same,  showing,  therefore,  the 
equality  of  the  pressures ;  but  if  an  aperture  of  the  same 
size  were  made  at  f,  the  quantity  would  be  found  corre- 
spondingly less. 

It  is  upon  these  principles  that  fountains  often  depend. 
The  water  in  a  reservoir  at  a  distance  is  brought  by  pipes 
Fig.  65.        to  the  jet  of  the  fountain,  and  there  suffered 
to  escape.     The  vertical  height  to  which  it 
can  be  thrown  is  as  the  height  of  the  reser- 
voir, and  by  having  several  jets  variously  ar- 
ranged in  respect  of  one  another,  the  fount- 
ain can  be  made  to  give  rise  to  different  fan- 
ciful forms,  as  is  the  case  with  the  public 
fountains  in  the  city  of  New  York. 

A  simple  method  of  exhibiting  the  fount- 
ain is  shown  in  Fig.  65.  A  jar,  G-,  is  filled 
with  water,  and  a  tube,  bent  as  at  a  b  c,  is 
dipped  in  it.  By  sucking  with  the  mouth  at 
«,  the  water  may  be  made  to  fill  the  tube, 
and  then,  on  being  left  to  itself,  will  play  as  a  fountain. 

On  similar  principles  we  account  for  the  occurrence  of 
springs,  natural  fountains,  and  Artesian  wells.  The  strata 
composing  the  crust  of  the  earth  are,  in  most  cases,  in  po- 
sitions inclined  to  the  horizon.  They  also  differ  very 
greatly  from  one  another  in  permeability  to  water — 
sandy  and  loamy  strata  readily  allowing  it  to  percolate 
through  them,  while  its  passage  is  more  perfectly  resisted 
by  tenacious  clays.  On  the  side  of  a  hill,  the  superficial 
strata  of  which  are  pervious,  but  which  rest  on  an  imper- 
vious bed  below,  the  rain  water  penetrates,  and  being 
guided  along  the  inclination,  bursts  out  on  the  sides  of  the 
hill  or  in  the  valley  below,  wherever  there  is  a  weak  place 
or  where  its  vertical  pressure  has  become  sufficiently  pow- 
erful to  force  a  way.  This  constitutes  a  common  spring. 

Prove  the  equality  of  vertical  and  lateral  pressures  by  the  instrument, 
Ftg.  64.  What  is  the  principle  of  fountains  ?  Describe  the  apparatus,  Fig. 
65.  On  what  principle  do  springs  flow  from  the  ground  ? 


ARTESIAN    WELLS.  59 

The  general  principle  of  the  Artesian  or  overflowing 
wells  is  illustrated  in  Fig.  66.  Let  b'  b  c  d,  be  the  sur- 
face of  a  region  of  country  the  strata  of  which,  b  b'  and 

Fig  66, 


a 


d  d',  are  more  or  less  impervious  to  water,  while  the  in- 
termediate one,  c  c,  of  a  sandy  or  porous  constitution,  al- 
lows it  a  freer  passage.  When  in  the  distant  sandy  coun- 
try at  c,  the  rain  falls,  it  percolates  readily  and  is  guided 
by  the  resisting  stratum,  d  d'.  Now  if  at  a,  a  boring  is 
made  deep  enough  to  strike  into  c  c  or  near  to  d  on  the 
principles  which  we  have  been  explaining,  the  water  will 
tend  to  rise  in  that  boring  to  its  proper  hydrostatic  level, 
and  therefore,  in  many  instances,  will  overflow  at  its 
mouth.  The  region  of  country  in  which  this  water  ori- 
ginally fell  may  have  been  many  miles  distant. 

It  follows,  from  the  action  of  gravity  on  liquids,  that  if 
we  have  several  which  differ  in  specific  gravity  in  the 
same  vessel,  they  will  arrange  themselves  according  to 
their  densities.  Thus,  if  into  a  deep  jar  we  pour  quick- 
silver, solution  of  sulphate  of  copper,  water,  and  alco- 
hol, they  will  arrange  themselves  in  the  order  in  which 
they  have  been  named. 

Wbat  are  Artesian  wells  ?  When  several  liquids  are  in  the  same  vessel, 
how  do  they  arrange  themselves  ? 


60  OF    FLOWING    LiaUIDS. 


LECTURE  XIII. 

OP  FLOWING  LIQUIDS  AND  HYDRAULIC  MACHINES. — Laws 
of  the  Flowing  of  Liquids. — Determination  of  the  Quan- 
tity Discharged. —  Contracted  Vein. — Parabolic  Jets. — 
Relative  Velocity  of  the  Parts  of  Streams. —  Undershot, 
Overshot,  Breast- Wheels. —  Common  Pump. — Forcing- 
Pump. —  Vera's  Pump. —  Chain-Pump. 

IF  a  liquid,  the  particles  of  which  have  no  cohesion, 
flows  from  an  aperture  in  the  bottom  of  its  containing  ves- 
sel, the  particles  so  descending  fall  to  the  aperture  with  a 
velocity  proportional  to  the  height  of  the  liquid. 

The  force  and  velocity  with  which  ,a  liquid  issues  de- 
pend, therefore,  on  the  height  of  its  level — the  higher  the 
level  the  greater  the  velocity. 

As  the  pressures  are  equal  in  all  directions,  and  as  it  is 
gravity  which  is  the  cause  of  the  flow,  "  The  velocity 
which  the  particles  of  a  fluid  acquire  when  issuing  from  an 
orifice,  whether  sideways,  upward,  or  downward,  is  equal 
to  that  which  they  would  have  acquired  in  falling  perpen- 
dicularly from  the  level  of  the  fluid  to  that  of  the  orifice." 

When  a  liquid  flows  from  a  reservoir  which  is  not  re- 
plenished, but  the  level  of  which  continually  descends, 
the  velocity  is  uniformly  retarded :  so  that  an  unreplen- 
ished  reservoir  empties  itself  through  a  given  aperture 
in  twice  the  time  which  would  have  been  required  for  the 
same  quantity  of  water  to  have  flowed  through  the  same 
aperture,  had  the  level  been  continually  kept  up  to  the 
same  point. 

The  theoretical  law  for  determining  the  quantity  of  wa- 
ter discharged  from  an  orifice,  and  which  is,  that  "  the 
quantity  discharged  in  each  second  may  be  obtained  by  mul- 
tiplying the  velocity  by  the  area  of  the  aperture"  is  not 
found  to  hold  good  in  practice — a  disturbance  arising  from 
the  adhesion  of  the  particles  to  one  another,  from  their 

On  what  does  the  velocity  of  a  flowing  liquid  depend  ?  What  is  that  ve- 
locity equal  to  ?  What  is  the  difference  of  flow  between  a  replenished  and 
an  unreplenished  reservoir  ?  Why  does  not  the  theoretical  law  for  the  dis- 
charge of  water  hold  good  ? 


THE    CONTRACTED    VEIN.  61 

friction  against  the  aperture,  and  from  the  formation  of 
what  is  designated  "the  contracted  vein."  For  when  wa- 
ter flows  through  a  circular  aperture  in  a  plate,  the  diam- 
eter of  the  issuing  stream  is  contracted  and  FI>.  67. 
reaches  its  minimum  dimensions  at  a-distance 
about  equal  to  that  of  half  the  diameter  of  the 
aperture,  as  at  s  s',  Fig.  67.  This  effect  arises 
from  the  circumstance  that  the  flowing  water  is 
not  alone  that  which  is  situated  perpendicularly 
above  the  orifice,  but  the  lateral  portions  likewise  move. 
These,  therefore,  going  in  oblique  directions,  make  the 
stream  depart  from  the  cylindrical  form,  and  contract  it, 
as  has  been  described. 

By  the  attachment  of  tubes  of  suitable  shapes  to  the  ap- 
erture, this  effect  may  be  avoided,  and  the  quantity  of 
flowing  water' very  greatly  increased.  A  simple  aperture 
and  such  a  tube  being  compared  together,  the  latter  was 
found  to  discharge  half  as  much  more  water  in  the  same 
space  of  time. 

As  the  motion  of  flowing  liquids  depends  on  the  same 
lav\s  as  that  of  falling  solids,  and  is  determined  by  gravi- 
ty, it  is  obvious  that  the  path  of  a  spouting  jet,  the  direc- 
tion of  which  is  parallel  or  oblique  to  the  horizon,  will  bo 
a  parabola ;  for,  as  we  shall  hereafter  see,  that  is  the  path 
of  a  body  projected  under  the  influence  of  gravity  in  vacuo. 
When  a  liquid  is  suffered  to  escape  in  a  horizontal  direc- 
tion through  the  side  of  a  vessel,  it  may  be  easily  shown 
to  flow  in  a  parabolic  path,  as  in  Fig.  68.  The  maximum 
distance  to  which  a  jet  can 
reach  on  a  horizontal  plane 
is,  when  the  opening  is  half 
the  height  of  the  liquid,  as 
at  C,  and  at  points  B  and  D 
equidistant  from  C,  it  spouts 
to  equal  distances. 

To.  measure  the  velocity 
of  flowing  water,  floating 
bodies  are  used  :  they  drift, 
immersed  in  the  stream  un- 
der examination.  A  bottle  ____. 

What  is  meant  by  the  "  contracted  vein  ?"  From  what  does  this  arise  ? 
How  may  the  quantity  of  flowing  water  be  increased?  What  is  the  path 
of  a  spouting  jet  ? 


62 


WATER-WHEELS. 


partly  filled  with  water,  so  that  it  will  sink  to  its  neck,  with 
a  small  flag  projecting,  answers  very  well;  or  the  num- 
ber of  revolutions  of  a  wheel  accommodated  with  float- 
boards  may  be  counted. 

Fig.  69.  In  any  stream  the  velocity  is  greatest 

in  the  middle  (wheve  the  water  is  deep- 
est), and  at  a  certain  distance  from  the 
surface.  From  this  point  it  diminishes 
toward  the  banks.  Investigations  of  this 
kind  are  best  made  by  Pictot's  stream- 
measurer,  Fig.  69.  It'  consists  of  a  ver- 


g  tube  corresponds  with  that  outside,  but 
|  the  impulse  of  a  stream  causes  the  water 
to  rise  in  the  tube  until  its  vertical  press- 
ure counterpoises  the  force. 

The  force  of  flowing  water  is  often 
employed  for  various  purposes  in  the 
arts.  We  have  several  different  kinds 
of  water-wheels,  as  the  undershot,  the 
overshot,  and  the  breast-wheel.  The 
first  of  these  consists  of  a  wheel  or 
drum  revolving  upon  an  axis,  and  on 
the  periphery  there  are  placed  float- 
boards,  a  b  c  d,  &c.  It  is  to  be  fixed 
so  that  its  lower  floats  are  immersed 
in  a  running  stream  or  tide,  and  is  driven  round  by  the 
momentum  of  the  current. 

Fig.  i\.  The  overshot-wheel,  in 

like  manner,  consists  of  a 
cylinder  or  drum,  with  a 
series  of  cells  or  buckets, 
so  arranged  that  the  water 
which  is  delivered  by  a 
trough,  A  B,  on  the  upper- 
most part  of  the  wheel, 
may  be  held  by  the  de- 
scending buckets  as  long  as  possible.  It  is  the  weight 

How  may  the  velocity  of  flowing  water  be  measured  ?  Describe  the 
stream-measurer.  What  is  the  undershot-wheel  ?  What  is  the  overshot- 
wheel? 


COMMON  PUMP. 


63 


Fig.  72. 


of   this  water   that  gives  motion   to  the  wheel   on  its 
axis. 

The  breast- wheel, 
in  like  manner,  con- 
sists of  a  drum  work- 
ing on  an  axis,  and 
having  float -boards 
on  its  periphery.  It 
is  placed  against  a 
wall  of  a  circular 
form,  and  the  water 
brought  to  it  fills  the  buckets  at  the  point  A,  and  turns 
the  wheel,  partly  by  its  momentum  and  partly  by  its  weight. 

Of  these  three  forms  the  overshot-wheel  is  the  most 
powerful.  i*g- 73- 

There  are  a  great  many  con- 
trivances for  the  purpose  of  rais- 
ing water  to  a  higher  level.  These 
constitute  the  different  varieties 
of  pumps. 

The  common  pump  is  repre- 
sented in  Fig.  73.  It  consists  of 
three  parts  :  the  suction-pipe,  the 
barrel,  and  the  piston.  The  suc- 
tion-pipe^e,  is  of  sufficient  length 
to  reach  down  to  the  water,  A, 
proposed  to  be  raised  from  the 
reservoir,  L.  The  barrel,  C  B,  is 
a  perfectly  cylindrical  cavity,  in 
which  the  piston,  G,  moves,  air- 
tight, up  and  down,  by  the  rod,  d. 
It  is  commonly  moved  by  a  lever, 
but  in  the  figure  a  rod  and  han- 
dle, D  E,  are  represented.  On  >^= 
one  side  is  the  spout,  F.  At  !\iHl 
the  top  of  the  suction-pipe,  at 
H,  there  is  a  valve,  b,  and  also 
one  on  the  piston,  at  a.  They 
both  open  upward.  When  the 
piston  is  raised  from  the  bottom 
of  the  barrel  and  again  depressed,  it  exhausts  the  air  in 

What  is  the  breast-wheel  ?     Which  of  these  is  the  most  powerful  ? 
Describe  the  lifting-pump. 


64 


THE    FORCING-PUMP. 


Fiff.  74. 


the  suction-pipe,  and  the  water  rises  from  the  reservoir, 
pressed  up  by  the  atmosphere.  After  a  few  movements 
of  the  piston  the  barrel  becomes  full  of  water,  which,  at 
each  successive  lift,  is  thrown  out  of  the  spout,  F.  The 
action  of  this  machine  is  readily  understood,  after  what 
has  been  said  of  the  air-pump,  which  it  closely  resembles 
in  structure. 

In  the  forcing-pump  the 
suction  pipe,  e  L,  is  commonly 
short,  and  the  piston,  g,  has 
no  valve.  On  the  box  at  H, 
there  is  a  valve,  b,  as  in  the 
former  machine,  and  when 
the  piston  is  moved  upward 
in  the  barrel,  C  B,  by  the 
handle,  E,  and  rod,  I)  d,  the 
water,  A,  rises  from  the  reser- 
voir, L,  and  enters  the  barrel. 
During  the  downward  move- 
ment of  the  piston  the  valve, 
b,  shuts,  and  the  water  passes 
by  a  channel  round  m,  through 
the  lateral  pipe,  M  O  M  N, 
into  the  air  vessel,  K  K.  The 
entrance  to  this  air-vessel  at 
P,  is  closed  by  a  valve,  #,  and 
there  proceeds  from  it  a  ver- 
tical tube,  H  G,  open  at  both 
ends.  After  a  few  movements 
of  the  piston,  the  lower  end, 
I,  of  this  tube  becomes  cov- 
ered with  water,  and  any  fur- 
ther quantity  now  thrown  in 
compresses  the  air  in  the  space,  H  G,  which,  exerting  its 
elastic  force,  drives  out  the  water  in  a  continuous  jet,  S. 
The  reciprocating  motion  of  the  piston  may,  therefore,  be 
made  to  give  rise  to  a  continuous  and  uriintermitting 
stream  by  the  aid  of  the  air-vessel,  K  K. 

Among  other  hydraulic  machines  may  be  mentioned 
Vera's  pump,  more,  however,  from  its  peculiar  construc- 
tion than  for  any  real  value  it  possesses.  It  consists  of  a 


Describe  the  forcing-pump. 


THE    CHAIN-PUMP. 


65 


.  75. 


pair  of  pulleys,  over  which  a  rope  is  made  to  run  rapidly, 
the  lower  one  is  immersed  in  the  wa- 
ter to  be  raised.  By  adhesion  a  por- 
tion of  the  water  follows  the  rope  in 
its  movements,  and  is  discharged  into 
a  receptacle  placed  above. 

The  chain-pump  consists  of  a  series 
of  flat  plates  held  together  by  pieces 
of  metal,  so  arranged  that,  by  turning 
an  upper  wheel,  the  whole  chain  is 
made  to  revolve,  on  one  side  ascending 
and  on  the  other  descending.  As  the 
flat  plates  pass  upward  .they  move 
through  a  trunk  of  suitable  shape,  and 
therefore  continually  lift  in  it  a  column 
of  water.  The  chain-pump  requires 
deep  water  to  work  in,  and  cannot  completely  empty  its 
reservoir,  but  it  has  the  advantage  of  not  being  liable  to 
be  choked. 


LECTURE  XIV. 

HYDRAULIC  MACHINES. — THEORY  OF  FLOTATION. — Archi- 
medes' Screw. —  The  Syphon  acts  by  the  Pressure  of 
Air. —  The  Descent,  Ascent,  and  Flotation  of  Solids  in 
Liquids. —  Quantity  of  Water  displaced  by  a  Floating 
Solid. — Case  where  fluids  of  different  densities  are  used. 
— Equilibrium  of  Floating  Solids. 

3f 

THE  screw  of  Archimedes  is  an  ancient  contrivance, 
invented  by  the  philosopher  whose  name  it  bears,  for  the 
purpose  of  raising  water  in  Egypt.  It  consists  of  a  hol- 
low screw-thread  wound  round  an  axis,  upon  which  it 
can  be  worked  by  means  of  a  handle.  The  lower  end  of 
this  spiral  tube  dips  in  the  reservoir  from  which  the  water 
is  to  be  raised,  and  by  turning  the  handle  the  water  con- 
tinually ascends  the  spire  and  flows  out  at  its  upper 
extremity. 

The  syphon  is  a  tube  with  two  branches,  C  E,  D  E, 

What  is  Vera's  pump  ?  Describe  the  chain-pump.  Describe  the  screw 
of  Archimedes.  What  is  a  syphon  ? 


66  THE    SYPHON. 

Fig.  76,  of  unequal  length,  often  employed  in  the  arts  for 
Fi    76  the  purpose  of  raising  or  decanting 

liquids.  The  method  of  using  it  is 
first  to  fill  it,  and  then  placing  the 
shorter  branch  in  the  vessel,  B,  to 
be  decanted,  the  liquid  ascends  to 
the  bend  and  runs  down  the  longer 
branch.  It  is  obvious  that  this  mo- 
tion arises  from  the  inequality  of 
weight  of  the  columns  in  the  two 
branches.  The  long  column  over- 
balances the  short  one,  and  deter- 
mines the  flow ;  but  this  cannot  take 
place  without  fresh  quantities  rising 
through  the  short  branch,  impelled  by  the  pressure  of  the 
air.  The  syphon,  therefore,  is  kept  full  by  the  pressure 
of  the  air,  and  kept  running  by  the  inequality  of  the 
lengths  of  the  columns  in  its  branches. 

This  inequality  is  not  to  be  measured  by  the  actual 
lengths  of  the  glass  branches  themselves,  but  it  is  to  be 
estimated  by  the  difference  of  level,  A,  of  the  liquid  in  the 
vessel  to  be  decanted  and  the  free  end,  D,  of  the  Syphon. 
That  this  instrument  acts  in  consequence  of  the  press- 
ure of  the  air  is  shown  by  making  a  small  one  discharge 
quicksilver  under  an  air-pump  receiver.  Its  action  will 
cease  as  soon  as  the  air  is  removed. 

By  the  aid  of  a  syphon  liquids  of  different  specific 
gravities  may  be  drawn  out  of  a  reservoir  without  dis- 
turbing one  another,  and  those  that  are  in  the  lower  part 
without  first  removing  those  above.  Upon  the  same  prin- 
ciple water  may  also  be  conducted  in  pipes  over  elevated 
grounds. 

Of  the  Floating  of  Bodies  in  Liquids. 

A  solid  substance  will  remain  motionless  in  the  interior 
of  a  liquid  mass  when  it  is  of  the  same  specific  gravity. 
Under  these  circumstances  the  forces  which  tend  to  make 
it  sink  are  its  own  weight  and  the  weight  of  the  column 

Why  does  water  ascend  in  its  short  branch?  Why  does  it  run  from 
the  longer  ?  How  is  the  inequality  of  the  branches  measured  ?  How  can 
it  be  proved  that  its  action  depends  on  the  pressure  of  the  air  ?  What  are 
the  uses  of  the  syphon  ?  Under  what  circumstances  will  a  solid  remain 
motionless  in  a  liquid? 


OF    FLOATING    BODIES.  67 

of  water  which  is  above  it.  But  as  its  weight  is  the  same 
as  that  of  an  equal  volume  of  the  liquid  in  which  it  is 
immersed,  this  downward  tendency  is  counteracted  and 
precisely  equilibrated  by  the  upward  pressure  of  the 
surrounding  liquid.  Consequently  the  solid  remains  mo- 
tionless in  any  position,  precisely  as  a  similar  mass  of  the 
liquid  itself  would  be. 

But  if  the  density  of  the  immersed  body  is  greater  than 
that  of  an  equal  bulk  of  the  liquid,  then  the  downward 
forces  preponderate  over  the  upward  pressure,  and  the 
solid  descends. 

If,  on  the  other  hand,  the  solid  is  lighter  than  an  equal 
volume  of  the  liquid,  the  upward  pressure  of  the  sur- 
rounding liquid  overcomes  the  downward  tendency,  and 
the  body  rises  to  the  surface  and  floats. 

In  the  act  of  floating,  the  body  is  divided  into  two 
regions  :  one  is  immersed  in  the  liquid  and  the  rest  is  in 
the  air.  The  part  which  is  immersed  under  the  surface 
of  the  liquid  is  such  as  displaces  a  quantity  of  that  liquid 
as  is  precisely  equal  in  weight  to  the. 
floating  solid.  This  may  be  proved 
experimentally.  Fill  a  glass,  A,  with 
water  until  it  runs  off  through  the  spout, 
a,  then  immerse  in  it  a  floating  body, 
such  as  a\ \vooden  ball;  the  ball  will 
displace  a  quantity  of  water,  which,  if  it 
be  collected  in  the  receiver,  B,  and 
weighed,  will  be  found  precisely  equal  to  the  weight  of 
the  wood. 

In  any  fluid  a  solid  body  will  therefore  sink  to  a  depth 
which  is  greater  as  its  specific  gravity  more  nearly  ap- 
proaches that  of  the  liquid.  As  soon  as  the  two  are  equal 
the  solid  becomes  wholly  immersed. 

In  fluids  of  different  densities  any  floating  body  sinks 
deeper  in  that  which  has  the  smallest  density.  It  will  be 
recollected  that  these  are  the  principles  which  are  in- 
volved in  the  action  of  hydrometers.  They  are  also 
applied  in  the  case  of  specific-gravity  bulbs,  which  are 
small  glass  bulbs,  with  solid  handles,  adjusted  by  the 

Under  what  will  it  rise,  and  under  what  will  it  sink  ?  What  portion  of 
the  floating  body  is  immersed  ?  How  may  this  be  proved  ?  How  do  the 
specific  gravities  of  the  solid  and  the  liquid  on  which  it  floats  affect  the 
phenomenon  ? 


68 


THE    BALL-COCK. 


maker,  so  as  to  be  of  different  densities.  When  a  num- 
ber of  these  are  put  into  a  liquid  some  will  float  and 
some  will  sink ;  but  the  one  which  remains  suspended, 
neither  floating  nor  sinking,  has  the  same  specific  gravity 
as  the  liquid.  That  specific  gravity  is  determined  by  the 
mark  engraved  on  the  bulb. 

When  a  body  floats  on  the  surface  of  water  it  tends  to 
take  a  position  of  stable  equilibrium.  The  principles 
brought  in  operation  here  will  be  more  fully  described 
when  we  come  to  the  study  of  the  center  of  gravity  of 
bodies.  For  the  present,  it  is  sufficient  to  state  that  sta- 
ble equilibrium  ensues  when  the  center  of  gravity  of  the 
floating  solid  is  in  the  same  vertical  line  as  the  center  of 
gravity  of  the  portion  of  fluid  displaced,  and  as  respects 
position  beneath  it.  These  considerations  are  of  great  im- 
portance in  the  art  of  ship -build  ing,  and  also  in  the  right 
distribution  of  the  cargo  or  ballast  of  a  ship. 

The  principle  of  flotation  is  in- 
geniously applied  in  the  ball-cock, 
an  instrument  for  keeping  cisterns 
or  boilers  filled  with  a  regulated 
amount  of  water.  Thus,  suppose 
that  m  n,  Fig.  78,  be  the  level  of 
the  water  in  the  boiler  of  a  steam- 
engine  ;  on  its  surface  let  there  float 
a  body,  B,  attached  by  means  of  a 
rod,  F  a,  to  a  lever,  a  c  b,  which 
works  on  the  fulcrum  c;  on  the 
other  side  of  the  lever,  at  b,  let 
there  be  attached,  by  the  rod  b  V,  a  valve,  V,  allowing 
water  to  flow  into  the  boiler,  through  the  feed-pipe,  V  O. 
Now,  as  the  level  of  the  water,  m  n,  in  the  boiler  lowers 
through  evaporation,  the  float,  B,  sinks  with  it,  and  de- 
presses the  end,  a,  of  the  lever ;  but  the  end,  b,  rising,  lifts 
the  valve,  V,  and  allows  the  water  to  go  down  the  feed- 
pipe; and  as  the  level  again  rises  in  the  boiler  the  valve,  V, 
again  shuts.  Instead  of  a  piece  of  wood  or  hollow  cop- 
per ball,  a  flat  piece  of  stone,  B,  is  commonly  used  ;  and 
to  make  it  float  it  is  counterpoised  by  a  weight,  W,  on 
the  opposite  arm  of  the  lever. 

How  are  specific-gravity  bulbs  used?  What  is  the  position  of  stable 
equilibrium  in  a  floating  body  ?  Describe  the  construction  and  action  of 
the  ball-cock. 


MOTION  AND    REST.  69 


OF  REST  AND  MOTION. 

MECHANICS. 

LECTURE   XV. 

MOTION  AND  REST. — Causes  of  Motion. — Classification  of 
Forces. — Estimate  of  Forces. — Direction  and  Intensity. 
—  Uniform  and  Variable  Motions. — Initial  and  Final 
Velocities. — Direct,  Rotatory,  and  Vibratory  Motions. 

ALL  objects  around  us  are  necessarily  in  a  condition 
either  of  motion  or  of  rest.  We  shall  soon  find  that  mat- 
ter has  not  of  itself  a  predisposition  for  one  or  other  of 
these  states ;  and  it  is  the  business  of  natural  philosophy 
to  assign  the  particular  causes  which  determine  it  to  either 
in  any  special  instance.  A  very  superficial  investigation 
soon  puts  us  on  our  guard  against  deception.  Things 
roay  appear  in  motion  which  are  at  rest,  or  at  rest  when 
in  reality  they  are  in  motion.  A  passenger  in  a  railroad 
car  sees  the  houses  and  trees  in  rapid  motion,  though  he 
is  well  assured  that  this  is  a  deception — a  deception  like 
that  which  occurs  on  a  greater  scale  in  the  apparent  rev- 
olution of  the  stars  from  east  to  west  every  night — the  true 
motion  not  being  in  them,  but  in  the  earth,  which  is  turn- 
ing in  the  opposite  direction  on  its  axis. 

If  deceptions  thus  take  place  as  respects  the  state  of 
motion,  the  same  holds  good  as  respects  the  state  of  rest. 
On  the  surface  of  the  earth  even  those  objects  which  seem 
to  us  to  be  quite  stationary  are  not  so  in  reality.  Natu- 
ral objects,  as  mountains  and  the  various  works  of  man, 
though  they  seem  to  maintain  an  unchangeable  relation  as 
respects  position  with  all  the  world  for  centuries  together, 
are  but  in  a  condition  of  RELATIVE  REST.  They  are,  of 

What  two  states  do  bodies  assume  ?  What  deceptions  may  occur  in  re- 
lation to  motion  and  rest  ?  What  is  meant  by  relative  and  what  by  abso- 
lute rest  ? 


70  MOTION    AND    REST. 

course,  affected  by  the  daily  revolution  of  the  earth  on  its 
axis,  arid  accompany  it  in  its  annual  movements  round  the 
sun.  Indeed,  as  respects  themselves,  their  parts  are  con- 
tinually changing  position.  Whatever  has  been  affected 
by  the  warmth  of  summer  shrinks  into  smaller  space 
through  the  cold  of  winter.  Two  objects  which  maintain 
their  position  toward  each  other  are  said  -to  be  at  rela- 
tive rest ;  but  we  make  a  wide  distinction  between  this 
and  absolute  rest.  All  philosophy  leads  us  to  suppose 
that  throughout  the  universe  there  is  not  a  solitary  parti- 
cle which  is  in  reality  in  the  latter  state. 

Whenever  an  object,  from  a  state  of  apparent  rest,  com- 
mences to  move,  a  cause  for  the  motion  may  always  be 
assigned.  And  inasmuch  as  such  causes  are  of  different 
kinds,  they  may  be  classified  as  primary  or  secondary 
motive  powers.  The  primary  motive  powers  are  utiiver^ 
sal  in  their  action.  Such,  for  instance,  as  the  general  at- 
tractive force  of  matter  or  GRAVITY.  The  secondary  are 
transient  in  their  effects.  The  action  of  animals,  of  elas- 
tic springs,  of  gunpowder,  are  examples.  Of  the  second- 
ary forces,  some  are  momentary  and  others  more  perma- 
nent, some  giving  rise  to  a  blow  or  shock,  and  some  to 
effects  of  a  continued  duration. 

Forces  may  be  compared  together  as  respects  their  in- 
tensities by  numbers  or  by  lines.  Thus  one  force  may  be 
five,  ten,  or  a  hundred  times  the  intensity  of  another,  and 
that  relation  be  expressed  by  the  appropriate  figures.  In 
the  same  manner,  by  lines  drawn  of  appropriate  length, 
we  may  exhibit  the  relation  of  forces ;  and  that  not  only 
as  respects  their  relative  intensity,  but  also  in  other  par- 
ticulars. The  direction  of  motion  resulting  from  the  appli- 
cation of  a  given  force  may  always  be  represented  by  a 
straight  line  drawn  from  the  point  at  which  the  motion 
commences  toward  the  point  to  which  the  moving  body 
is  impelled.  The  point  at  which  the  force  takes  effect 
upon  the  body  is  termed  the  point  of  application ;  and 
the  direction  of  motion  is  the  path  in  which  the  body 
moves.  To  this  special  designations  are  given  appropri- 

Is  any  object  in  nature  in  a  state  of  absolute  rest  ?  How  may  motive 
powers  be  classified  ?  What  are  primary  motive  powers  ?  Give  examples 
of  some  that  are  secondary.  How  may  forces  be  compared  together  ? 
How  may  forces  be  represented  ?  What  is  meant  by  the  point  of  appli- 
cation? 


DIFFERENT    KINDS    OF    MOTION.  71 

ate  to  the  nature  of  the  case,  such  as  curvilinear,  rectilin- 
ear, &c. 

Moving  bodies  pass  over  their  paths  with  different  de- 
grees of  speed.  One  may  pass  through  ten  feet  in  a  sec- 
ond of  time,  and  another  through  a  thousand  in  the  same 
interval.  We  say,  therefore,  that  they  have  different  ve- 
locities. Such  estimates  of  velocity  are  obviously^  ob- 
tained by  comparing  the  spaces  passed  over  in  a  given 
unit  of  time.  The  unit  of  time  selected  in  natural  phi- 
losophy is  one  second. 

A  moving  body  may  be  in  a  state  of  either  uniform  or 
variable  motion.  In  the  former  case  its  velocity  contin- 
ually remains  unchanged,  and  it  passes  over  equal  dis- 
tances in  equal  times.  In  the  latter  its  velocity  under- 
goes alterations,  and  the  spaces  over  which  it  passes  in 
equal  times  are  different.  If  the  velocity  is  on  the  in- 
crease it  is  spoken  of  as  a  uniformly  accelerated  motion. 
If  on  the  decrease  as  a  uniformly  retarded  motion.  In 
these  cases  we  mean  by  the  term  initial  velocity  the  ve- 
locity which  the  body  had  when  it  commenced  moving, 
as  measured  by  the  space  it  would  then  have  passed  over 
in  one  second ;  and,  by  the  final  velocity,  that  which  it  pos- 
sessed at  the  moment  we  are  considering  it  measured  in 
the  same  way.  The  flight  of  bomb-shells  upward  in  the 
air  is  an  instance  of  retarded  motion  ;  their  descent  down- 
ward of  accelerated  motion.  The  movement  of  the  fingers 
of  a  clock  is  an  example  of  uniform  motion. 

There  are  motions  of  different  kinds :  1st,  direct ;  2d, 
rotatory ;  3d,  vibratory. 

1st.  By  direct  motion  we  mean  that  in  which  all  the 
parts  of  the  whole  body  are  advancing  in  the  same  direc- 
tion with  the  same  velocity. 

2d.  By  rotatory  motion  we  imply  that  some  parts  of  the 
body  are  going  in  opposite  directions  to  others.  The 
axis  of  rotation  is  an  imaginary  line,  round  which  tho 
parts  of  the  body  turn,  it  being  itself  at  rest. 

3d.  By  vibratory  movement  we  mean  that  the  body 
which  changes  its  place  returns  toward  its  original  posi' 
lion  with  a  motion  in  the  opposite  direction.  Thus,  the 

How  are  velocities  measured  ?  What  is  the  unit  of  time  ?  What  \i 
meant  by  uniform  and  what  by  variable  motion  ?  What  by  initial  and 
final  velocity?  What  varieties  of  motion  are  there?  What  is  direct 
motion  ?  What  is  rotatory  motion  ?  What  is  vibratory  motion  ? 


72  COMPOUND    MOTION. 

particles  of  water  which  form  waves  alternately  rise  and 
sink,  and  the  pendulum  of  a  clock  beats  backward  and 
forward.  These  are  examples  of  vibratory  or  oscillatory 
movement. 


LECTURE  XVI. 

OP  THE  COMPOSITION  AND  RESOLUTION  OF  FORCES. — 
Compound  Motion. — Equilibrium.  —  Resultant.  —  The 
Parallelogram  of  Forces. — Case  where  there  are  more 
Forces  than  Two.  —  Parallel  Forces.  —  Resolution  of 
Forces.  —  Equilibrium  of  three  Forces.  —  Curvilinear 
Motions. 

WHEN  several  forces  act  simultaneously  on\a  body,  so 
as  to  put  it  in  motion,  that  motion  is  said  to  be  com- 
pound. 

In  cases  of  compound  motion,  if  the  component  or  con- 
stituent forces  all  act  in  the  same  direction,  the  resulting 
effect  will  be  equal  to  the  sum  of  all  those  forces  taken 
together. 

If  the  constituent  forces  act  in  opposite  directions,  the 
resulting  effect  will  be   equal    to   their  difference,   and 
Fig.  79.  its  direction  will  be  that  of  the 

greater  force.  Thus,  if  to  a 
knot,  a,  Fig.  79,  we  attach  sev- 
eral weights,  b  c,  by  means,,  of  a 
string  passing  over  a  pulley,  e, 
these  weights  will  evidently  tend 
to  pull  the  knot  from  a  to  e.  But 
sf  if  to  the  same  knot  we  attach  a 
weight,j£  by  a  string  passing  over 
the  pulley  g,  this  tends  to  draw- 
it  in  the  opposite  direction.  When  the  weights  on  each 
side  of  the  knot  act  conjointly,  they  tend  to  draw  it  oppo- 
site ways,  and  it  moves  in  the  direction  of  the  greater 
force. 

What  is  compound  motion?  When  the  component  forces  all  act  in  the 
same  direction,  what  is  their  effect  equal  to?  What  is  the  result  when 
they  act  in  opposite  directions  ?  Under  what  circumstances  are  forces  in 
equilibrio  ? 


PARALLELOGRAM    OF    FORCES.  73 

If  two  forces  of  equal  intensity,  but  in  opposite  direc- 
tions, act  upon  a  given  point,  that  point  remains  motion- 
less, and  the  forces  are  said  to  be  in  (equilibria.  When 
there  are  many  forces  acting  upon  a  point  in  equilibrio, 
the  sum  of  all  those  acting  on  one  side  must  be  equal  to 
the  sum  of  all  the  rest  which  act  in  the  opposite  direction. 

By  the  resultant  of  forces  we  mean  a  single  force  which 
would  represent  in  intensity  and  direction  the  conjoint 
action  of  those  forces. 

If  the  constituent  forces  neither  act  in  the  same  nor  in 
opposite  directions,  but  at  an  angle  to  each  other,  their 
resultant  can  be  found  in  the  following  manner  : — 

Let  a  be  the  point  on  which  Fig.  so. 

the  forces  act ;  let  one  of  them  be  ft 

represented  in  intensity  and  di-  —  .^ff- ^ 

rection  by  the  line  a  b,  and  the 
other  likewise  in  intensity  and 
direction  by  the  line  a  c.  Draw 
the  lines  b  d,  c  d,  so  as  to  com- 
plete the  parallelogram  a  b  c  d  ;  fc m 

draw  also  the  diagonal,  a  d.    This  c 

diagonal  will  be  the  resultant  of  the  two  forces,  and  will, 

therefore,  represent  their  conjoint  action  in  intensity  and 

direction. 

The    operation    of 
pairs  of  forces  upon  a 

point  is  readily  under-  t^a,  . . , 

stood.  Thus,  1st.  On  * 
a  point,  a,  Fig.  81,  let 
two  forces,  a  b,  a  c,  act.  Complete  the  parallelogram 
a  b  d  c,  and  draw  its  diagonal,  a  d.  This  line  will  rep- 
resent in  intensity  and  direction  the  resultant  force. 
2d.  On  a  point,  a,  Fig.  82,  Fig.  m. 

let  two  forces  again  repre- 
sented in  intensity  and  di- 
rection by  the  lines  a  b,  a  c, 
act.  Complete  the  paral- 
lelogram abed,  draw  its  diagonal,  a  d,  which  is  the 
resultant,  as  before.  Now,  on  comparing  Fig.  81  with 
Fig.  82,  it  readily  appears  that  the  resultant  of  two  forces 

What  is  meant  by  a  resultant  ?  Describe  the  parallelogram  of  forces. 
Give  illustrations  of  the  case  in  which  the  forces  act  nearly  in  the  same, 
and  also  of  that  in  which  they  act  nearly  in  opposite  directions. 

D 


74 


ANGULAR    AND    PARALLEL    FORCES. 


is  greater  as  those  forces  act  more  nearly  in  the  same 
direction,  and  less  as  those  forces  act  more  nearly  in 
opposite  directions. 

Many  popular  illustrations  of  the  parallelogram  of 
forces  might  be  cited.  The  following  may,  however, 
suffice.  If  a  boat  be  rowed  across  a  river  when  there  is 
no  current,  it  will  pass  in  a  straight  line  from  bank  to 
bank  perpendicularly  ;  but  this  will  not  take  place  if  there 
is  a  current,  for  as  the  boat  crosses  it  is  drifted  by  the 
stream,  and  makes  the  opposite  bank  at  a  point  which  is 
lower  according  as  the  stream  is  more  rapid.  It  moves 
in  a  diagonal  direction. 

On  the  same  principles  we  can  determine  the  common 
resultant  of  many  forces  acting  on 
a  point.  Two  of  the  forces  are 
first  taken  and  their  resultant  found. 
This  resultant  is  combined  with  the 
third  force,  and  a  second  resultant 
found.  This  again  is  combined 
with  the  fourth  force,  and  so  on,  un- 
til the  forces  are  exhausted.  The 
final  resultant  represents  the  con- 
joint action  of  all. 

Thus,  let  there  be  three  forces  applied  to  the  point  «, 
represented  in  intensity  and  direction  by  the  lines  a  b, 
ac,ad,  Fig.  S3,  respectively  ;  if  a  b  and  a  c  be  combined, 
they  give  as  their  resultant  a  e,  and  if  this  resultant,  a  e,  be 
combined  with  the  third  force,  a  d,  it  yields  the  resultant 
af,  which,  therefore,  represents  the  common  action  of  all 
three  forces. 

The  resultant  of  two  paral- 
lel forces  applied  to  a  line,  and 
on  the  same  side  of  it,  is  equal  to 
their  sum  and  parallel  to  their 
direction.  Thus,  the  forces  a 
b,  a'  b'  applied  to  the  line  a  a', 
give  a  resultant,  p  r,  parallel 
to  their  common  direction  and 
equal  to  their  sum. 


a 


Fig  84. 
P 


Give  an  illustration  of  the  diagonal  motion  of  a  body  under  the  influence 
two  forces.  How  may  the  resultant  of  more  forces  than  two  be  found  ? 
hat  is  the  resultant  of  parallel  forces  applied  to  a  line  on  the  same,  and 


of  two  forces 
What 


RESOLUTION    OF    FORCES.  75 

But  when  parallel  forces  are  applied  on  opposite  sides 
of  a  line,  the  resultant  is  equal  to  their  difference,  and  its 
direction  is  parallel  to  theirs.  In  this,  as  also  in  the  fore- 
going case,  the  point  at  which  the  resultant  acts  is  at  a 
distance  from  the  points  at  which  the  two  forces  act, 
inversely  proportional  to  their  intensities.  In  the  fore- 
going case  this  point  falls  between  the  directions  of  the 
two  forces,  and  in  the  latter  on  the  outside  of  the  direction 
of  the  greater  force. 

The  parallelogram  of  forces  not  Pig-  85. 

only  serves  to  effect  the  composi- 
tion of  several  forces,  but  also  the 
resolution  of  any  given  force  ;  that 
is  to  assign  several  forces  which  in 
their  intensities  and  directions  shall 
be  equivalent  to  it.  Thus,  let  a  J] 
Fig.  85,  be  the  given  force;  by 
making  it  the  diagonal  of  a  paral- 
lelogram it  may  be  resolved  into  its  components,  a  d,  a  e  ; 
in  the  same  manner,  a  et  may  be  resolved  into  its  compo- 
nents, a  c,  a  b.  Thus,  therefore,  the  original  force  is 
resolved  into  three  components,  a  b,  a  c,  a  d. 

Upon  similar  principles  it  may  be  readily  proved  that 
two  forces  acting  at  any  angle  upon  a  point  can  never 
maintain  that  point  in  equilibrio — but  three  forces  may ; 
and  in  this  instance,  they  will  be  represented  in  intensity 
and  direction  by  the  three  sides  of  a  triangle,  perpendic- 
ular to  their  respective  directions. 

If  two  forces  act  upon  a  point  in  the  direction  of  and  in 
magnitude  proportional  to  the  sides  of  a  parallelogram, 
that  point  will  be  kept  in  equilibrio  by  a  third  force  op- 
posed to  them  in  the  direction  of  the  diagonal  and  pro- 
portional to  it.  On  the  table,  a  d,  place  a  circular  piece  of 
paper,  on  which  there  is  drawn  any  triangle,  a  b  c,  c  coin- 
ciding with  the  center  of  the  table;  and  let  us  suppose 
that  the  sides  of  this  triangle  are,  as  shown  in  the  figure, 
in  the  proportion  to  one  another,  as  2  3  4 ;  draw  upon  the 
paper,  c  e,  parallel  to  a  b,  and  prolong  a  c  to  d.  Take  three 
strings,  making  a  knot  at  the  point  c,  and  by  means  of  the 

What  is  meant  by  the  resolution  of  forces  ?  How  does  the  parallelogram 
of  forces  serve  for  this  purpose  ?  Can  two  forces  acting  at  an  angle  upon 
a  point  keep  it  in  equilibrio?  Can  three?  In  this  case  what  must  be 
their  relation  ? 


76 


COMPOSITION    OF    FORCES. 


Fig.  86. 


movable  pullies,  1 1 1,  stretch  the 
strings  over  the  lines  c  b,  c  d,  c 
e ;  at  the  end  of  c  d  suspend  a 
weight  of  four  pounds,  at  the 
end  of  c  e  one  of  three  pounds, 
and  at  the  end  of  c  b  one  of  two 
pounds.  The  knot  will  remain 
in  equilibrio,  proving,  there- 
fore, the  proposition. 

In  the  composition  of  forces ' 
power  must  always  be  lost. 
Thus,  in  this  experiment  we 
see  that  a  weight  of  three 
pounds  and  one  of  two  pounds 
equipoise  a  weight  of  four  pounds  only. 

If  of  two  forces  acting  upon  a  point  one  is  momentary 
and  the  other  constant,  the  point  may  move  in  a  curve. 
Thus,  if  in  Fig.  87,  a  shot  be  projected  obliquely  up- 
*• 87-  ward  from  a  gun,  it  is  under  the  ac- 

tion of  two  forces — the  momentary 
force  of  the  explosion  of  the  gun- 
powder and  the  constant  effect  of 
the  attraction  of  the  earth.  It- 
describes,  therefore,  a  curvilinear 
path,  a  b  c,  the  direction  of  which 
continually  declines  toward  the  di- 
rection of  the  constant  force. 
It  is  only  when  a  force  acts  in  a  direction  perpendicu- 
lar to  a  body  that  its  full  effect  is  obtained.  This  is  easi- 
ly proved  by  resolving  an  oblique  force  into  two  others, 
one  of  which  is  perpendicular  and  the  other  parallel  to 
the  side  of  the  body  acted  upon.  This  latter  force  is,  of 
course,  lost. 

Why  in  the  composition  of  forces  is  power  always  lost  ?  What  is  the 
result  of  the  action  of  a  momentary  and  a  constant  force  upon  a  point? 
In  what  direction  must  a  force  act  to  obtain  its  full  effect  ? 


INERTIA.  77 


LECTURE  XVII. 

INERTIA. — Inertia  a  Properly  of  Matter. — Indifference  to 
Motion  and  Rest. — Moving  Masses  are  Motive  Powers. 
— Determination  of  the  Quantity  of  Motion. — Momen- 
tum.— Action  and  Reaction. — Newton's  Laws  of  Mo- 
tion.— Bohnenbcrger's  Machine. 

ALL  bodies  have  a  tendency  to  maintain  their  present 
condition,  whether  it  be  of  motion  or  rest.  It  is  only  by 
the  exertion  of  force  that  that  condition  can  be  changed. 
A  mass  of  any  kind,  when  at  rest,  resists  the  application 
of  force  to  put  it  in  motion,  and  when  in  motion  resists 
any  attempt  to  bring  it  to  rest.  This  property  is  termed 
INERTIA.  It  is  illustrated  by  many  familiar  instances : 
thus,  loaded  carriages  require  the  exertion  of  far  more 
force  to  put  them  in  motion  than  is  subsequently  required 
to  keep  them  going,  and  a  train  of  railroad  cars  will  run 
for  a  great  distance  after  the  locomotive  is  detached. 

Universal  experience  shows  that  inanimate  bodies  have 
no  power  to  produce  spontaneous  changes  in  their  con- 
dition. They  are  wholly  inactive.  Even  when  in  motion 
they  exhibit  no  tendency  whatever  to  alter  their  state. 
Thus,  the  earth  rotates  on  its  axis  at  the  same  rate  which 
it  did  thousands  of  years  ago,  and  the  planetary  bodies 
pursue  their  orbits  with  an  unchangeable  velocity.  A 
moving  mass  can  neither  increase  nor  diminish  its  rate  of 
speed,  for  if  it  could  do  the  former  it  must  necessarily 
have  the  power  spontaneously  to  put  itself  in  motion  if  it 
were  in  a  condition  of  rest.  Nor  can  such  a  mass,  if  in 
motion,  change  the  direction  of  its  movement  any  more 
than  it  can  change  its  velocity.  Such  a  change  of  direc- 
tion would  imply  the  operation  of  some  innate  force,  which 
of  itself  could  have  put  the  mass  in  movement.  When- 
ever, therefore,  we  discover  in  a  moving  body  changes  in 
direction  or  changes  in  velocity,  we  at  once  impute  them 

What  is  meant  by  the  term  inertia  ?  Give  an  illustration  of  inertia. 
What  illustration  have  we  that  when  bodies  are  in  motion  they  do  not 
spontaneously  tend  to  come  to  rest?  Can  a  moving  mass  increase  or  di- 
minish its  rate  of  speed  ?  Can  it  change  its  direction  of  itself? 


78  MOMENTUM. 

to  the  agency  of  acting  forces,  and  not  to  any  innate  power 
of  the  moving  body  itself. 

Fig.  88.  If  an  ivory  ball,  a,  Fig.  88, 

be  laid  upon  a  sheet  of  paper, 

® b  c,  on  the  table,  and  the  paper 

c      suddenly  pulled  away,  the  ball 

does  not  accompany  the  movement  but  remains  in  the 
same  place  on  the  table. 

A  person  jumping  from  a  carriage  in  rapid  motion  falls 
down,  because  his  body,  still  participating  in  the  motion 
of  the  carriage,  follows  its  direction  after  his  feet  have 
struck  the  earth. 

By  the  MASS  of  a  body  we  mean  the  quantity  of  mat- 
ter contained  in  it — that  is,  the  sum  of  all  its  particles. 
The  mass  of  a  body  depends  on  its  volume  and  density. 

In  consequence  of  their  inertia,  masses  in  motion  are 

themselves  motive  powers.     Such  a  mass  impinging  on  a 

Fig.  89.  second  tends  to  set  it  in   motion. 

_  Thus,  if  a  ball  a,  Fig.  89,  moving 

W         i         W toward  c,  impinge  upon  a  second 

ball,  b,  of  equal  weight,  the  two 

will  move  together  toward  c,  with  a  velocity  one  half  of 
that  which  a  originally  had.  In  this  case,  therefore,  a  has 
acted  as  a  motive  force  upon  Z»,  and  it  is  obvious  that  the 
intensity  of  this  action  must  depend  on  the  magnitude 
and  velocity  of  a,  increasing  as  they  increase  and  dimin- 
ishing as  they  diminish.  The  ball  a  is  said,  therefore,  to 
have  a  certain  momentum  or  moment,  which  depends  part- 
ly upon  its  mass  and  partly  upon  its  velocity;  and  the  mo- 
ments of  any  two  bodies  may  be  compared  by  multiplying 
together  the  mass  and  velocity  of  each.  Thus,  if  a  body, 
A,  has  twice  the  mass  of  another,  B,  and  moves  with  the 
same  velocity,  the  momentum  of  A  will  be  twice  that  of 
B  ;  but  if  A,  having  twice  the  mass  of  B,  has  only  half 
its  velocity  the  moments  of  the  two  will  be  equal. 

It  is  upon  this  principle  that  heavy  masses  moving  very 
slowly  exert  a  great  force,  and  that  bodies  comparatively 
light,  moving  with  great  speed,  produce  striking  effects. 
The  battering-rams  of  the  ancients,  which  were  heavy 
masses  moving  slowly,  did  riot  produce  more  powerful 

Give. an  experimental  illustration  of  inertia.  How  is  it  that  moving 
bodies  are  themselves  motive  powers  ?  How  is  the  quantity  of  motion  or 
momentum  of  a  body  ascertained  ? 


ACTION    AND    REACTION. 


79 


effects  than   cannon-shot,  which,  though   comparatively 
light,  move  with  prodigious  speed. 

From  the  foregoing  considerations,  it  therefore  appears 
that  the  amount  of  motion  depends  neither  upon  the  mass 
alone  nor  the  velocity  alone.  A  certain  mass,  A,  moving 
with  a  given  velocity,  has  a  certain  momentum  or  quanti- 
ty of  motion.  If  to  A  a  second  equal  mass,  B,  with  a  sim- 
ilar velocity  be  added,  the  two  conjointly  will,  of  course, 
possess  double  the  momentum  of  the  first — the  mass  has 
doubled,  though  the  speed  is  the  same,  and  therefore  the 
quantity  of  motion  has  doubled.  Again,  if  a  certain  mass, 
A,  moves  with  a  given  speed,  and  a  second  one,  B,  moves 
with  a  double  speed,  it  is  obvious  that  this  last  will  have 
twice  the  quantity  of  motion  of  the  former.  Here  the 
masses  are  the  same,  but  the  velocities  are  different.  The 
quantity  of  motion  or  momentum  which  a  body  possesses 
is,  therefore,  obtained  by  multiplying  together  the  num- 
bers which  express  its  mass  and  its  velocity. 

Action  and  reaction  are  always  equal  to  each  other. 
The  resistance  which  a  given  body  exhibits  is  equal  to 
the  effect  of  any  force  operating  upon  it.  This  equality 
of  action  and  reaction  may  be  shown  by  an  apparatus 
represented  in  Fig.  90,  in  which  Fis-  90- 

two  balls  of  clay  or  putty,  a  b, 
are  suspended  by  strings  so  as  to 
move  over  a  graduated  arc.  If 
one  of  the  balls  be  allowed  to  fall 
upon  the  other,  through  a  given 
number  of  degrees,  it  will  com- 
municate to  it  a  pait  of  its  mo- 
tion, and  the  following  facts  may 
be  observed  :  1st.  The  bodies,  af- 
ter collision,  move  on  together,  and  therefore  have  the  same 
velocity.  2d.  The  quantity  of  motion  remains  unchang- 
ed, the  one  having  gained  as  much  as  the  other  has  lost, 
so  that  if  the  two  are  equal  they  will  have  half  the  veloc- 
ity after  impact  that  the  moving  one  had  when  alone. 
3d.  If  equal,  and  moving  in  opposite  directions  with  equal 
velocities,  they  will  destroy  each  other's  motions  and  come 

Does  the  mass  or  the  velocity,  taken  alone,  measure  the  amount  of  mo- 
tion T  What  is  the  relation  between  action  and  reaction  ?  What  is  the 
apparatus  represented  in  Fig.  90  intended  to  illustrate  ?  Mention  some  01 

the  results. 


80  NEWTON'S  LAWS. 

to  rest.  4th.  If  unequal,  and  moving  in  opposite  direc- 
tions, they  will  come  to  rest  when  their  velocities  are  in- 
versely as  their  masses. 

The  following  three  propositions  are  called  "Newton's 
laws  of  motion."  They  contain  the  results  depending  on 
inertia : — 

I.  Every  body  must  persevere  in  its  state  of  rest  or  of 
uniform  motion  in  a  straight  line,  unless  it  be  compelled 
to  change  that  state  by  forces  impressed  upon  it. 

II.  Every  change  of  motion  must  be  proportional  to 
the  impressed  force,  and  must  be  in  the  direction  of  that 
straight  line  in  which  the  force  is  impressed. 

III.  Action  must  always  be  equal,  and  contrary  to  re- 
action, or  the  action  of  two  bodies  upon  each  other  must 
be  equal  and  directed  to  contrary  sides. 

As  an  example  of  the  operation  of  inertia,  and  illustra- 
ting the  invariability  of  position  of  the  axLs  of  the  earth 
during  its  revolution,  I  here  describe 
Bohnenberger's  machine.  It  consists 
of  three  movable  rings,  A  A  A,  Fig. 
91,  placed  at  right  angles  to  each  other, 
AJj  {^jjfl  Jf  and  in  the  smallest  ring  there  is  a  heavy 
metal  ball,  B,  supported  on  an  axis, 
which  also  bears  a  little  roller,  c.  A 
thread  being  wound  round  this  roller 
and  any  particular  position  being  given 
to  the  axis,  by  quickly  pulling  the 
thread  the  ball  may  be  set  in  rapid  ro- 
tation. It  is  now  immaterial  in  what  position  the  instru- 
ment is  placed,  its  axis  continually  maintains  the  same  di- 
rection, and  the  ring  which  supports  it  will  resist  a  con- 
siderable pressure  tending  to  displace  it. 

What  are  Newton's  three  laws  of  motion?  Describe  Bohnenberger's 
machine.  What  does  it  illustrate  ? 


GRAVITATION.  81 


LECTURE  XVIII. 

GRAVITATION. — Preliminary  Ideas  of  Motions  of  Attrac- 
tion.—  The  Earth  and  Falling  Bodies. — Laics  of  At- 
traction, as  respects  Mass  and  Distance.  —  Nature  of 
Weight. — Absolute  and  Specific  Weight. —  The  Plumb- 
Line. — Convergence  of  suck  Lines  toward  the  Earth's 
Center. — Action  of  Mountain  Masses. 

ALL  material  substances  exert  upon  each  other  an  at- 
tractive force.  To  this  the  designation  of  GRAVITY  or 
GRAVITATION  has  been  given.  It  was  the  great  discovery 
of  Sir  I.  Newton  that  the  same  force  which  produces  the 
descent  of  a  stone  to  the  ground  holds  together  the  plan- 
ets and  other  celestial  bodies. 

To  obtain  a  preliminary  idea  of  the  nature  and  opera- 
tion of  this  force,  let  us  suppose  that  two  balls  of  equal 
weight  be  placed  in  presence  of  each  other,  and  under 
such  circumstances  that  no  extraneous  agency  supervenes 
to  interfere  with  their  mutual  action.  Under  these  cir- 
cumstances, all  the  phenomena  of  nature  prove  that  the 
two  balls  will  commence  moving  toward  each  other  with- 
equal  speed,  their  velocity  continually  increasing  until 
they  come  in  contact.  Inasmuch,  therefore,  as  their 
masses  are  equal  and  their  velocities  equal,  the  quantities 
of  motion  they  respectively  possess  will  also  be  equal,  as 
is  proved  in  Lecture  XVII. 

Again,  let  there  be  two  other  balls  situated  as  before, 
but  let  one  of  them,  B,  be  twice  as  large  Fig.  92. 

as  A.  Motion  will  again  ensue  by  reason 
of  their  mutual  attraction,  and  they  will  ^^ 
approach  each  other  with  a  velocity  con-  ® 
tinually  increasing.  In  this  instance, 
however,  their  speed  will  not  be  equal,  the  larger  body, 
B,  having  a  correspondingly  less  velocity  than  the  smaller 
one,  A.  If,  as  we  have  supposed,  it  is  twice  as  large,  its 

What  is  meant  by  gravity  ?  Give  an  explanation  of  the  phenomena  of 
the  attraction  of  two  equal  balls.  Give  a  similar  explanation  in  the  case 
where  the  balls  are  unequal. 


82  LAWS    OF    GRAVITATION. 

velocity  will  be  only  one  half.  But  in  this,  as  in  the 
former  case,  the  quantity  of  motion  that  each  possesses 
is  the  same,  for  that  depends  on  velocity  and  mass  con- 
jointly. 

Further,  if  of  the  two  bodies  one  becomes  infinitely 
great  as  respects  the  other,  then  it  is  obvious  that  the  lit- 
tle one  alone  will  appear  to  move.  This  condition  is  what 
actually  obtains  in  the  case  of  our  earth  and  bodies  sub- 
jected to  its  influence.  A  mass  of  any  kind,  the  support 
of  which  is  suddenly  removed,  falls  at  once  to  the  ground, 
and  though  in  reality  the  earth  moves  to  meet  it  just  as 
much  as  it  moves  to  meet  the  earth,  the  difference  in 
these  masses  is  so  immeasurably  great  that  the  earth's 
motion  is  imperceptible  and  may  be  wholly  neglected. 

The  force  by  which  bodies  are  thus  solicited  to  move 
to  the  earth  is  called  terrestrial  gravity  or  gravitation. 

The  force  of  gravity  depends  on  two  different  condi- 
tions:  1st,  the  mass;  2d,  the  distance. 

1st.  The  intensity  of  the  force  of  gravity  is  directly  as 
the  mass.  That  is  to  say,  that,  for  example,  in  the  case 
of  the  earth,  if  its  mass  were  twice  as  large  its  force  of 
attraction  would  be  twice  as  great ;  or  if  it  were  only  half 
as  large  its  attraction  would  be  only  half  as  much  as  it  is. 

2d.  In  common  with  all  other  central  forces,  gravity 
diminishes  as  the  distance  increases.  The  law  which  de- 
termines this  is  expressed  as  follows:  "  The  force  of 
gravity  is  inversely  as  the  square  of  the  distance ;"  that 
is  to  say,  if  a  body  be  placed  two,  three,  four,  five  times 
its  original  distance  from  another,  the  force  attracting 
it  will  continually  diminish,  and  in  those  different  instances 
will  successively  be  four,  nine,  sixteen,  twenty-five  times 
less  than  at  first. 

When  a  body,  instead  of  being  allowed  to  fall  freely  to 
the  earth,  is  supported,  its  tendency  to  descend  is  not  anni- 
hilated, but  it  exerts  upon  the  supporting  surface  a  degree 
of  pressure.  This  pressure  we  speak  of  as  WEIGHT.  And 
inasmuch  as  the  attractive  force  upon  a  body  depends  on 
its  mass,  it  is  obvious  that,  if  the  mass  is  doubled,  the 
weight  is  doubled  ;  if  the  mass  is  tripled,  the  weight  is 

What  is  the  relation  in  this  respect  between  falling  bodies  and  the  earth  ? 
On  what  two  conditions  does  the  intensity  of  gravity  depend  ?  What  is 
the  law  for  the  mass?  What  is  the  law  for  the  distance?  What  is 


ABSOLUTE    AND   SPECIFIC    WEIGHT.  83 

tripled.  Or,  in  other  words,  the  weight  of  bodies  is  al- 
ways proportional  to  their  mass. 

The  absolute  weight  of  a  given  body  at  the  same  place 
on  the  earth's  surface  is  always  the  same ;  for  the  mass, 
and,  therefore,  the  attractive  force  of  the  earth  never 
changes.  If  by  any  means  the  attractive  influence  of  the 
earth  could  be  doubled,  the  weight  of  every  object  would 
change,  and  be  doubled  correspondingly. 

The  absolute  weight  of  bodies  is  determined  by  bal- 
ances, springs,  steelyards,  and  other  such  contrivances,  as 
will  be  explained  in  their  proper  place.  Different  units 
of  weight  are  adopted  in  different  countries,  and  for  dif- 
ferent purposes,  as  the  grain,  ounce,  pound,  gramme,  &c. 

In  bodies  of  the  same  nature  the  absolute  weight  is  pro- 
portional to  the  volume.  Thus  a  mass  of  iron  which  is 
twice  the  volume  of  another  mass  will  also  have  twice  its 
weight. 

But  when  we  examine  dissimilar  bodies  the  result  is 
very  different.  A  globe  of  water  compared  with  one  of 
copper,  or  lead,  or  wood  of  the  same  size  will  have  a  very 
different  weight.  The  lead  will  weigh  more  than  the 
water,  and  the  wood  less. 

This  fact  we  have  already  pointed  out  by  the  term 
"specific  gravity,"  or  specific  weight  of  bodies.  And, 
inasmuch  as  it  is  obviously  a  relative  thing  or  a  matter  of 
comparison,  it  is  necessary  to  select  some  substance  which 
shall  serve  to  compare  other  bodies  with  :  for  solids  and 
liquids  water  is  taken  as  the  unit  or  standard  of  compari- 
son. And  we  say  that  iron  is  about  seven,  lead  eleven, 
quicksilver  thirteen  times  as  heavy  as  it ;  or  that  they 
have  specific  gravities  expressed  by  those  numbers.  The 
unit  of  comparison  for  gaseous  and  vaporous  bodies  is 
atmospheric  air. 

When  an  unsupported  body  is  allowed  to  fall  its  path 
is  in  a  vertical  line.  If  a  body  be  suspended  by  a  thread 
the  thread  represents  the  path  in  which  that  body  would 
have  moved.  It  occupies  a  vertical  direction,  or  is  per- 
pendicular to  the  position  which  would  be  occupied  by 

Is  it  constant  for  the  same  body  ?  How  is  absolute  weight  determined  ? 
What  units  are  employed  ?  What  connection  is  there  between  weight 
and  volume  in  bodies  of  the  same  kind  ?  What  is  meant  by  specific  grav- 
ity ?  What  substance  is  the  unit  for  solids  and  liquids  ?  What  is  the 
unit  for  gases  and  vapors  ? 


84  THE    PLUMB-LINE. 

a  surface  of  stagnant  water.  Such  a  thread  is  termed  a 
plumb-line.  It  is  of  constant  use  in  the  arts  to  determine 
horizontal  and  vertical  lines. 

Fig.  93.  If  in  two  positions,  A  B,  Fig.  93,  on 

the  earth's  surface  plumb-lines  were  sus- 
pended, it  would  be  found  that,  though 
they  are  perpendicular  as  respects  that 
surface,  they  are  not  parallel  to  one  an- 
other, but  incline,  at  a  small  angle,  A  C 
B,  to  each  other.  If  their  distance  be  one 
mile  this  convergence  would  amount  to 
one  minute;  and  if  it  be  sixty  miles  the 
convergence  would  be  one  degree.  Now, 
as  the  plumb-line  indicates  the  path  of  a  falling  body,  it 
is  easily  understood  that  on  different  parts  of  the  earth's 
surface  the  paths  of  falling  bodies  have  the  inclinations 
just  described.  A  little  consideration  shows  that  the  de- 
scent of  such  bodies  is  in  a  line  directed  to  the  center,  C, 
of  the  earth. 

That  center  we  may  therefore  regard  as  the  active 
point,  or  seat  of  the  whole  earth's  attractive  influence. 

When  examinations  with  plumb-lines  are  made  in  the 
neighborhood  of  mountain  masses  those  masses  exert  a 
disturbing  agency  on  the  plummet,  drawing  the  line 
from  its  true  vertical  position.  But  this  is  nothing  more 
than  what  ought  to  take  place  on  the  theory  of  universal 
gravitation  ;  for  that  theory  asserting  that  all  masses  ex- 
ert an  attractive  influence,  the  results  here  pointed  out 
must  necessarily  ensue,  and  the  lateral  action  of  the  moun- 
tains correspondingly  draw  the  plummet  aside. 

What  is  a  plumb-line  ?  At  considerable  distances  from  one  another  are 
plumb-lines  parallel?  What  conclusion  is  drawn  from  this  fact ?  What 
is  the  effect  of  mountain  masses  ? 


OF    FALLING    BODIES.  85 


LECTURE  XIX. 

THE  DESCENT  OF  FALLING  BODIES. — Accelerated  Motion. 
— Different  bodies  fall  with  equal  velocities. — Laws  of 
Descent  as  respects  Velocities,  Spaces,  Times. — Prin- 
ciple of  Atticood's  Machine. — It  verifies  the  Laws  of 
Descent — Resistance  of  the  Atmosphere. 

OBSERVATION  proves  that  the  force  with  which  a  falling 
body  descends  depends  upon  the  distance  through  which 
it  has  passed.  A  given  weight  falling  through  a  space  of 
an  inch  or  two  may  give  rise  to  insignificant  results ;  but 
if  it  has  passed  through  many  yards  those  results  become 
correspondingly  greater. 

Gravity  being  a  force  continually  in  operation,  a  falling 
body  must  be  under  its  influence  during  the  whole  period 
of  its  descent.  The  soliciting  action  does  not  take  effect 
at  the  first  moment  of  motion  and  then  cease,  but  it  con- 
tinues all  the  time,  exerting  as  it  were  a  cumulative  effect. 
The  falling  body  may  be  regarded  as  incessantly  receiv- 
ing a  rapidly  recurring  series  of  impulses,  all  tending  to 
drive  it  in  the  same  direction.  The  effect  of  each  one  is, 
therefore,  added  to  those  of  all  its  predecessors,  and  a  uni- 
formly accelerated  motion  is  the  result. 

Falling  bodies  are,  therefore,  said  to  descend  with  a  uni- 
formly accelerated  motion. 

As  the  attraction  of  the  earth  operates  with  equal  in- 
tensity on  all  bodies,  all  bodies  must  fall  with  equal  ve- 
locities. A  superficial  consideration  might  lead  to  the 
erroneous  conclusion  that  a  heavy  body  ought  to  descend 
more  quickly  than  a  lighter.  But  if  we  have  two  equal 
masses,  apart  from  each  other,  falling  freely  to  the  ground, 
they  will  evidently  make  their  descent  in  equal  times  or 
with  the  same  velocity.  Nor  will  it  alter  the  case  at  all 
if  we  imagine  them  to  be  connected  with  each  other  by 
an  inflexible  line.  That  line  can  in  no  manner  increase 
or  diminish  their  time  of  descent. 

What  is  the  difference  of  effect  when  bodies  have  fallen  through  differ- 
ent spaces  ?  Why  does  gravity  produce  an  accelerated  motion  '?  "Do  all 
bodies  fall  to  the  earth  with  the  same  or  different  velocities  ? 


86  LAWS    OF    FALLING    BODIES. 

The  space  through  which  a  body  falls  in  one  second  of 
time  varies  to  a  small  extent  in  different  latitudes.  It  is, 
however,  usually  estimated  at  sixteen  feet  and  one  tenth. 

As  the  effect  of  gravity  is  to  produce  a  uniformly 
accelerated  motion,  the  final  velocities  of  a  descending  body 
will  increase  as  the  times  increase  ;  thus,  at  the  end  of  two 
seconds,  that  velocity  is  twice  as  great  as  at  one ;  at  the 
end  of  three  seconds,  three  times  as  great ;  at  the  end  of 
four,  four  times,  and  so  on.  Therefore  the  final  velocity 
at  the  end 

Of  the  first  second  is  ...  32|  feet. 

"    second    "  ...  64|    " 

"      third      "  ...  96|    " 

&c.,  &c. 

The  spaces  through  which  the  body  descends  in  equal 
successive  portions  of  time  increase  as  the  numbers  1.3.5.7, 
&c. ;  that  is  to  say,  as  the  body  descends  through  sixteen 
feet  and  one  tenth  in  the  first  second,  the  subsequent 
spaces  will  be 

For  the  first  second 

"    second    "  ... 

"      third     "  ... 

&c., 

and  these  numbers  are  evidently  as  1.3.5,  &c. 

The  entire  space  through  which  a  body  falls  increases  as 
the  squares  of  the  times.  Thus,  the  entire  space  is, 

For  the  first  second  .        .        .        IGy^feet. 
"     second    "  64  f     " 

"      third      "  ...      144T^-    " 
&c.,  &c. 

and  these  numbers  are  evidently  as  1.4.9,  &c.,  which  are 
themselves  the  squares  of  the  numbers  1.2.3,  &c. 

If  a  body  continued  falling  with  the  final  velocity  it  had 
acquired,  after  falling  a  given  time,  and  the  operation  of 
gravity  were  then  suspended,  it  would  descend  in  the  same, 
length  of  time  through  twice  the  space  it  fell  through  before 
relieved  from  the  action  of  gravity . 

Is  the  space  through  which  a  body  descends  every  where  the  same  ? 
What  is  the  relation  between  final  velocities  and  times  ?  What  relation 
is  there  between  the  spaces  and  times  ?  What  between  the  entire  spaces 
and  times?  Suppose  a  body  continues  to  fall,  gravity  being  suspended, 
what  is  the  relation  of  the  space  through  which  it  will  move  with  that  it 
has  already  fallen  through,  the  times  being  equal? 


ATWOOD'S  MACHINE.  87 

The  following  table  imbodiee  the  results  of  the  three 
first  laws. 

Times 1.2.3.4.5.6.7,  &c. 

Final  velocities 2.4.6.8.10.12.14,  &c 

Space  for  each  time      ....  1.3.5.7.9.11.13,  &c. 

Whole  spaces 1.4.9.16.25.3G.49,  &c. 

It  would  not  be  easy  to  confirm  these  results  by  ex- 
periments directly  made  on  falling  bodies,  the  space 
described  in  the  first  second  being  so  great  (more  than 
sixteen  feet),  and  the  spaces  increasing  as  the  squares  of 
the  times.  There  is  an  instrument,  however,  known  as 
Attwood's  machine,  in  which  the  force  of  gravity  being 
moderated  without  any  change  in  its  essential  characters, 
we  are  enabled  to  verify  the  foregoing  laws. 

The  principle  of  Attwood's  machine  is  this.  Over  a 
pulley,  A,  Fig.  94,  let  there  pass  a  fine  silk  Fig.  94. 
line  which  suspends  at  its  extremities  equal 
weights,  b  c.  These  weights,  being  equally 
acted  upon  by  gravity,  will,  of  course,  have 
no  disposition  to  move  ;  but  now  to  one  of  the 
weights,  c,  let  there  be  added  another  much 
smaller  weight,  d,  these  conjointly  prepon- 
derating over  b,  will  descend,  b  at  the  same 
time  rising.  It  might  be  supposed  that  the 
small  additional  weight,  d,  under  these  cir- 
cumstances, would  fall  as  fast  as  if  it  were 
unsupported  in  the  air ;  but  we  must  not  forget  that  it  has 
simultaneously  to  bring  down  with  it  the  weight  to  which 
it  is  attached,  and  also  to  lift  the  opposite  one.  By  its 
gravity,  therefore,  it  does  descend,  but  with  a  velocity 
which  is  less  in  proportion  as  the  difference  between  the 
two  weights  to  which  it  it  affixed  is  less  than  their  sum. 
It  gives  us  a  force  precisely  like  gravity — indeed  it  is 
gravity  itself — operating  under  such  conditions  as  to  allow 
a  moderate  velocity. 

To  avoid  friction  of  the  axle  of  the  pulley,  each  of  its 
ends  rests  upon  two  friction-wheels,  as  is  shown  at  Q, 
Fig.  95  ;  P  is  the  pillar  which  supports  the  pulley.  Oue 
of  the  weights  is  seen  at  &,  the  other  moves  in  front  of 
the  divided  scale  c  d.  This  last  weight  is  made  to  pre- 

What  is  the  principle  of  Attwood's  machine  ?  Why  does  not  the  addi- 
tional weight  fall  as  fast  as  if  it  fell  freely  ?  Describe  the  construction  of 
the  machine. 


88 


ATTWOOD  S    MACHINE. 


Fig.  95. 


ponderate  by  means  of  a  rod.  There  is  a  shelf  which 
can  be  screwed  opposite  any  of  the  di- 
visions of  the  scale,  and  the  arrival  of 
the  descending  weight  at  that  point  is 
indicated  by  the  sound  arising  from 
its  striking.  A  clock,  R,  indicates 
the  time  which  has  elapsed.  To  en- 
able us  to  fulfill  the  condition  of  sus- 
pending the  action  of  gravity  at  any 
moment,  a  shelf,  in  the  form  of  a  ring, 
is  screwed  upon  the  scale  at  the  point 
required.  Through  this  the  descend- 
ing weight  can  freely  pass,  but  the 
rod  which  caused  the  preponderance 
is  intercepted.  The  equality  of  the 
two  weights  is,  therefore,  reassumed, 
and  the  action  of  gravity  virtually  sus- 
pended. 

By  this  machine  it  may  be  shown 
that,  in  order  that  the  descending 
weight  shall  strike  the  ring  at  inter- 
vals of  1,  2,  3,  4,  &c.,  seconds,  count- 
ing from  the  time  at  which  its  fall 
commences,  the  ring  must  be  placed 
at  distances  from  the  zero  of  the  scale, 
which  are  as  the  numbers  1,  4,  9,  16, 


&c. ;  and  t  ese  are  the  squares  of  the  times.  And  in  the 
same  manner  may  the  other  laws  of  the  falling  of  bodies 
be  proved. 

When  a  body  is  thrown  vertically  upward  it  rises  with 
an  equably  retarded  motion,  losing  32}  feet  of  its  original 
velocity  every  second.  If  in  vacuo,  it  would  occupy  as 
much  time  in  rising  as  in  falling  to  acquire  its  original 
velocity,  and  the  times  expended  in  the  ascent  and  descent 
would  be  the  same. 

Forces  which,  like  gravity,  in  this  instance,  produce  a 
retardation  of  motion  are  nevertheless  designated  as  ac- 
celerating forces.  Their  action  is  such  that,  if  it  were 
brought  to  bear  on  a  body  at  rest,  it  would  give  rise  to  an 
accelerated  motion. 


Give  an  illustration  of  its  use.  What  is  the  effect  when  a  body  is  thrown 
vertically  upward  ?  Under  what  signification  is  the  term  "  accelerating 
forces"  sometimes  used  ? 


RESISTANCE    OF    THE    AIR. 


89 


In  rapid  movements  taking  place  in  the  atmosphere,  a 
disturbing  agency  arises  in  the  resistance  of  Fig.  96. 
the  air — a  disturbance  which  becomes  the 
more  striking  as  the  descending  body  is 
lighter,  or  exposes  more  surface.  If  a  piece 
of  gold  and  a  feather  are  suffered  to  drop 
from  a  certain  height,  the  gold  reaches  the 
ground  much  sooner  than  the  feather.  Thus,, 
if  in  a  tall  air-pump  receiver  we  allow,  by 
turning  the  button,  a,  Fig.  96,  a  gold  coin  and 
a  feather  to  drop,  the  feather  occupies  much 
longer  than  the  coin  in  effecting  its  descent ; 
and  that  this  is  due  to  the  resistance  of  the 
air  is  proved  by  withdrawing  the  air  from 
the  receiver,  and,  when  a  good  vacuum  is 
obtained,  making  the  coin  and  the  feather 
fall  again.  It  will  now  be  found  that  they 
descend  in  the  same  time  precisely. 
,,  Nor  is  it  alone  light  bodies  which  are  subject  to  this 
disturbance  :  it  is  common  to  all.  Thus  it  was  found  that 
a  ball  of  lead  dropped  from  the  dome  of  St.  Paul's  Cathe- 
dral, in  London,  occupied  4£  seconds  in  reaching  the 
pavement,  the  distance  being  272  feet.  But  in  that  time 
it  should  have  fallen  324  feet,  the  retardation  being  due 
to  the  resistance  of  the  air. 

It  has  been  observed  that  the  force  of  gravity  is  not 
the  same  on  all  parts  of  the  earth. 
The  distance  fallen  through  in 
one  second  at  the  pole  is  16'12 
feet ;  but  at  the  equator  it  is 
16*01  feet.  This  arises  from  the 
circumstance,  that  the  earth  is 
not  a  perfect  sphere,  its  polar 
diameter  being  shorter  than  its 
equatorial  and,  therefore,  bodies 
at  the  poles  are  nearer  to  its 
center  than  they  are  at  the  equator.  ThusV  in  Fig.  97, 
let  N  S  represent  the  globe  of  the  earth,  N  and  S  being 


What  cause  interferes  with  these  results  ?  How  can  it  be  proved  that 
these  effects  are  due  to  the  resistance  of  the  air  ?  Is  this  disturbance  lim- 
ited to  light  bodies '!  What  is  the  distance  through  which  a  falling  body 
descends  at  the  equator  and  at  the  poles  ?  What  is  the  reason  of  this 
difference? 


90  MOTION    ON    PLANES. 

the  north  and  south  poles,  respectively.  Owing  to  its 
polar  being  shorter  than  its  equatorial  diameter,  bodies 
situated  at  different  points  on  the  surface  may  be  at  very 
different  distances  from  the  center,  and  the  force  of  grav- 
ity exerted  upon  them  may  be  correspondingly  very  dif- 
ferent. 


LECTURE  XX. 

MOTION  ON  INCLINED  PLANES. — Case  of  a  Horizontal,  a 
Vertical,  and  an  Inclined  Plane. —  Wright  expended 
partly  in  producing  pressure  and  partly  motion. — Laws 
of  Descent  down  Inclined  Planes. — Systems  of  Planes. 
— Ascent  up  Planes. 

PROJECTILES. — Parabolic  theory  of  Projectiles. — Disturb- 
ing agency  of  the  Atmosphere. — Resistance  to  Cannon- 
shot. — Ricochet. — Ballistic  Pendulum. 

WHEN  a  spherical  body  is  placed  on  a  plane  set  hori- 
zontally, its  whole  gravitation  is  expended  in  producing  a 
pressure  on  that  plane.  If  the  plane  is  set  in  a  vertical 
position  the  body  no  longer  presses  upon  it,  but  descends 
vertically  and  unresisted.  At  all  intermediate  positions 
which  may  be  given  to  the  plane  the  absolute  attraction 
will  be  partly  expended  in  producing  a  pressure  upon 
that  plane,  and  partly  in  producing  an  accelerated  de- 
scent. The  quantities  of  force  thus  relatively  expended 
in  producing  the  pressure  and  the  motion  will  vary  with 
the  inclination  of  the  plane  :  that  portion  producing  press- 
ure increasing  as  the  plane  becomes  more  horizontal,  and 
that  producing  motion  increasing  as  the  plane  becomes 
more  vertical. 

Let  there  be  a  ball  descending  on  the  surface  of  an  in- 
clined plane,  A  B,  Fig.  98,  and  let  the  line  d  e  represent 
its  weight  or  absolute  gravity.  By  the  parallelogram  of 
forces  we  may  decompose  this  into  two  other  forces,  df 

What  are  the  phenomena  exhibited  by  a  spherical  body  placed  on  planes 
of  different  inclinations?  Into  what  forces  may  the  absolute  gravity  of 
the  body  be  resolved  ? 


MOTION    DOWN    INCLINED    PLANES.  91 

and  d  g,  one  of  which  is 
perpendicular  to  the  plane 
and  the  other  parallel  to 
it.  The  first,  therefore,  is 
expended  in  producing 
pressure  upon  the  plane, 
and  the  second  in  pro- 
ducing motion  down  it. 

The  following  are  the  laws  of  the  descent  of  bodies 
down  inclined  planes. 

The  pressure  on  the  inclined  plane  is  to  the  weight  of 
the  body  as  the  base,  B  C,  of  the  inclined  plane  is  to  its 
length,  A  B. 

The  accelerated  motion  of  a  descending  body  is  to  that 
which  it  would  have  had  if  it  fell  freely  as  the  height,  A 

C,  of  the  plane  is  to  its  length,  A  B. 

The  final  velocity  which  the  descending  body  acquires 
is  equal  to  that  which  it  would  have  had  if  it  had  fallen 
freely  through  a  distance  equal  to  the  height  of  the  plane  ; 
and,  therefore,  the  velocities  acquired  on  planes  of  equal 
height,  but  unequal  inclinations,  are  equal. 

The  space  passed  through  by  a  body  falling  freely  is  to 
that  gone  over  an  inclined  plane,  in  equal  times,  as  the 
length  of  the  plane  is  to  its  height. 

If  a  series  of  inclined  planes  be  represented,  in  position 
and  length,  by  the  chords  of  a  circle  termi-       Fig.  99 
rating  at  the  extremity  of  the  vertical  diame- A 
ter,  the  times  of  descent  down  each  will  be 
equal,  and  also  equal  to  the  time  of  descent 
through  that  vertical  diameter.     Thus,  let  A 

D,  A  G,  D  B,  G  B  be  chords  of  a  circle  ter- 
minating at  the  extremities,  A  B,  of  the  ver- 
tical diameter;  and,  regarding  these  as  inclin- 
ed planes,  a  body  will  descend  from  A  to  D, 
or  A  to  G,  or  D  to  B,  or  G  to  B  in  the  same 
time  that  it  would  fall  from  A  to  B. 

If  a  body  descend  down  a  system  of  several  planes,  A 


What  effects  do  those  forces  respectively  produce  ?  What  relation  is 
there  between  the  pressure  on  the  inclined  plane  and  the  weight  of  the 
body  ?  What  is  the  relation  between  the  velocities  in  descent  down  a 
plane  and  free  falling  ?  What  is  the  final  velocity  equal  to  ?  What  is  the 
relation  of  the  space  passed  through  ?  What  is  Fig.  99  intended,  to  illus- 
trate ? 


92  PROJECTILES. 

C,  Fig.   100,  with  different  inclinations,  it  will  acquire 
Fig.  100.  the  same  velocity  as  it  would  have 

had  in  descending  through  the  same 
vertical  height,  A  B,  though  the 
times  of  descent  are  unequal. 

If  a  body  which  has  descended 
an  inclined  plane  meets  at  the  foot 
of  it  a  second  plane  of  equal  alti- 
tude, it  will  ascend  this  plane  with 
the  velocity  acquired  in  coming 
C  "  down  the  first,  until  it  has  reached 
the  same  altitude  from  which  it  descended.  Its  velocity 
being  now  expended,  it  will  re-descend,  and  ascend  the  first 
plane  as  before,  oscillating  down  one  plane,  up  the  other, 
and  then  back  again.  The  same  thing  will  take  place 
if,  instead  of  being  over  an  inclined 
plane,  the  motion  be  made  over  a 
curve,  as  in  Fig.  101.  In  practice, 
however,  the  resistance  of  the  air 
and  friction  soon  bring  these  motions  to  an  end. 

In  the  motions  of  projectiles  two  forces  are  involved — 
the  continuous  action  of  gravity,  and  the  momentary  force 
which  gave  rise  to  the  impulse — such  as  muscular  ex- 
ertion, the  explosion  of  gunpowder,  the  action  of  a 
spring,  &c. 

The  resulting  effects  of  the  combination  of  these  forces 
will  differ  with  the  circumstances  under  which  they  act. 
If  a  body  be  projected  downward,  in  a  vertical  line,  it  fol- 
lows its  ordinary  course  of  descent,  its  accelerated  motion 
arising  from  gravity  being  conjoined  to  the  original  pro- 
jectile force.  But  if  it  be  thrown  vertically  upward,  the 
action  of  gravity  is  to  produce  a  uniform  retardation. 
Its  velocity  becomes  less  and  less,  until  finally  it  wholly 
ceases.  The  body  then  descends  by  the  action  of  the 
earth,  the  time  of  its  descent  being  equal  to  that  of  its  as- 
cent, its  final  velocity  being  equal  to  its  initial  velocity. 

But  if  the  projectile  force  forms  any  angle  with  the 
direction  of  gravity,  the  path  of  the  body  is  in  a  para- 
bolic curve,  as  seen  in  Fig.  102.  If  the  direction  of 

Describe  the  phenomena  of  motion  on  curves.  What  forces  are  involv- 
ed in  the  motion  of  a  projectile  ?  What  are  the  effects  in  vertical  projec- 
tion upward  and  downward?  What  is  the  theoretical  path  in  angular 
projection  ? 


PARABOLIC    THEORY.  93 

the  projection  be  horizontal,  the 
path  described  will  be  half  a  para- 
bola. 

This,  which  passes  under  the  title 
of  the  parabolic  theory  of  projec- 
tiles, is  found  to  be  entirely  de- 
parted from  in  practice.  The  curve 
described  by  shot  thrown  from  guns 
is  not  a  parabola,  but  another  curve, 
the  Ballistic.  In  vertical  projections,  instead  of  the  times 
of  ascent  and  descent  being  equal,  the  former  is  less.  The 
final  velocity  is  not  the  same  as  the  initial,  but  less.  Nor 
is  the  descending  motion  uniformly  accelerated  ;  but,  after 
a  certain  point,  it  is  constant.  Analogous  differences  are 
discovered  in  angular  projections. 

The  distance  through  which  a  projectile  could  go  upon 
the  parabolic  theory,  with  an  initial  velocity  of  2000  feet 
per  second,  is  about  24  miles :  whereas  no  projectile  has 
even  been  thrown  farther  than  five  miles. 

In  reality,  the  parabolic  theory  of  projectiles  holds  only 
for  a  vacuum.  And  the  atmospheric  air,  exerting  its 
resisting  agency,  totally  changes  all  the  phenomena — not 
only  changing  the  path,  but  whatever  may  have  been  the 
initial  velocity,  bringing  it  speedily  down  below  1280  feet 
per  second. 

The  cause  of  this  phenomenon  Fis- 103> 

may  be    understood  from  Fig. 

103.     Let  B  be  a  cannon-ball,     5^ft 

moving  from  A  to  C  with  a  ve-   A- B^g  C 

locity  more  than  2000  feet  per 
second.     In  its  flight  it  removes  a 

column  of  air  between  A  and  B,  and  as  the  air  flows  into 
a  vacuum  only  at  the  rate  of  1280  feet  per  second,  the 
ball  leaves  a  vacuum  behind  it.  In  the  same  manner  it 
powerfully  compresses  the  air  in  front.  This,  therefore, 
steadily  presses  it  into  the  vacuum  behind,  or,  in  other 
words,  retards  it,  and  soon  brings  its  velocity  down  to 
such  a  point  that  the  ball  moves  no  faster  than  the  air 
moves — that  is,  1280  feet  per  second. 

Is  this  the  path  in  reality  ?  Mention  some  of  the  discrepancies  between 
the  theoretical  and  actual  movements  of  projectiles.  What  are  these  dis- 
crepancies due  to?  Describe  the  nature  of  the  resistance  exerted  on  a 
cannon-shot  in  its  passage  through  the  air. 


94 


MOTION    ROUND    A    CENTER. 


Fig.  104. 


A  shot  thrown  with  a  high  initial  velocity  not  only  de- 
viates from  the  parabolic  path,  but  also  to  the  right  and 
left  of  it,  perhaps  several  times.  A  ball  striking  on  the 
earth  or  water  at  a  small  angle,  bounds  forward  *or  rico- 
chets, doing  this  again  and  again  until  its  motion  ceases. 

The  initial  velocity  given 
by  gunpowder  to  a  ball,  and, 
therefore,  the  explosive  force 
of  that  material  may  be  de- 
termined by  the  Ballistic  pen- 
dulum. This  consists  of  a 
heavy  mass,  A,  Fig.  104,  sus- 
pended as  a  pendulum,  so  as 
to  move  over  a  graduated  arc. 
Into  this,  at  the  center  of  per- 
cussion, the  ball  is  fired.  The 
pendulum  moves  to  a  corresponding  extent  over  the  grad- 
uated arc,  with  a  velocity  which  is  less  according  as  the 
weight  of  the  ball  and  pendulum  is  greater  than  the 
weight  of  the  ball  alone. 

The  explosive  force  of  gunpowder  is  equal  to  2000  at- 
mospheres. It  expands  with  a  velocity  of  5000  feet  per 
second,  and  can  communicate  to  a  ball  a  velocity  of  2000 
feet  per  second.  The  velocity  is  greater  with  long  than 
short  guns,  because  the  influence  of  the  powder  on  the 
ball  is  longer  continued. 


LECTURE  XXI. 

OF  MOTION  ROUND  A  CENTER. — Peculiarity  of  Motion  on 
a  Curve. —  Centrifugal  Force. — Conditions  of  Free  Cur- 
vilinear Motion. — Motion  of  the  Planets. — Motion  in  a 
Circle. — Motion  in  an  Ellipse. — Rotation  on  an  Axis. — 
Figure  of  Revolution. — Stability  of  the  Axis  of  Rota- 
tion. 

IN  considering  the  motion  of  bodies  down  inclined 
planes,  we  have  shown  that  the  action  of  gravity  upon 

What  is  meant  by  ricochet?  Describe  the  ballistic  pendulum.  What 
is  the  estimate  of  the  explosive  force  of  gunpowder  ?  What  is  the  veloci- 
ty of  its  expansion  ?  What  is  the  velocity  it  can  communicate  to  a  ball  ? 


MOTION    ON    A    CURVE.  95 

them  may  be  divided  into  two  portions — one  producing 
pressure  upon  the  plane,  and  therefore  acting  perpendic- 
ularly to  its  surface;  the  other  acting  parallel  to  the  plane, 
and  therefore  producing  motion  down  it. 

It  has  also  been  shown  that,  in  some  respects,  there  is  an 
analogy  between  movements  over  inclined  planes  and  over 
curved  lines,  but  a  further  consideration  proves  that  be- 
tween the  two  there  is  also  a  very  important  difference.  A 
pressure  occurs  in  the  case  of  a  body  moving  on  a  curve 
which  is  not  found  in  the  case  of  one  moving  on  a  plane. 
It  arises  from  the  inertia  of  a  moving  body.  Thus,  if  a 
body  commences  to  move  down  an  inclined  plane,  the 
force  producing  the  motion  is,  as  we  have  seen,  parallel 
to  the  plane.  From  the  first  moment  of  motion  to  the 
.last  the  direction  is  the  same,  and  inasmuch  as  the  inertia 
of  the  body,  when  in  motion,  tends  to  continue  that  mo- 
tion in  the  same  straight  line,  no  deflecting  agency  is  en- 
countered. 

But  it  is  very  different  with  Fig.  105. 

motion  on  a  curve.  Here  the 
direction  of  descent  from  A  to 
B  is  perpetually  changing  ;  the 
curve  from  its  form  resists,  and 
therefore  deflects  the  falling 
body.  At  any  point  its  inertia 
tends  to  continue  its  motion  in 
a  straight  line  :  thus,  at  A,  were 
it  not  for  the  curve  it  would 
move  in  the  line  A  a,  at  B  in 
the  line  B  b,  these  lines  being  tangents  to  the  curve  at  the 
points  A  and  B.  The  curve,  therefore,  continually  de- 
flecting the  falling  body,  experiences  a  pressure  itself — a 
pressure  which  obviously  does  not  occur  in  the  case  of 
an  inclined  plane.  This  pressure  is  denominated  "  cen- 
trifugal force,"  because  the  moving  body  tends  to  fly  from 
the  center  of  the  curve. 

In  the  foregoing  explanation  we  have  regarded  the 
body  as  being  compelled  to  move  in  a  curvilinear  path, 
by  means  of  an  inflexible  and  resisting  surface.  But  it 
may  easily  be  shown  that  the  same  kind  of  motion  will 

Explain  the  difference  between  motion  on  inclined  planes  and  motion  on 
curves.  What  is  meant  by  centrifugal  force  ?  Under  what  circumstances 
can  curvilinear  motion  ensue  without  the  intervention  of  a  rigid  curve  ? 


96 


CURVILINEAR    MOTION. 


Fig.  106. 


ensue  without  any  such  compelling  or  resisting  surface, 
provided  the  body  be  under  the  control  of  two  forces, 
one  of  which  continually  tends  to  draw  it  to  the  cen- 
ter of  the  curve  in  which  it  moves,  while  the  other,  as 
a  momentary  impulse,  tends  to  carry  it  in  a  different  di- 
rection. 

Thus,  let  there  be  a 
body,  A,  Fig.  106,  attract- 
ed by  another  body,  S, 
and  also  subjected  to  a 
projectile  force  tending 
to  carry  it  in  the  direction 
A  H.  Under  the  con- 
joint influence  of  the  two 
forces  it  will  describe  a 
curvilinear  orbit,  A  T  W. 
The  point  to  which  the 
first  force  solicits  the 
body  to  move  is  termed 
the  center  of  gravity- — 
that  force  itself  is  desig- 
nated the  centripetal  force,  and  the  momentary  force 
passes  under  the  name  of  tangential  force. 

The  following  experiment 
clearly  shows  how,  under 
the  action  of  such  forces, 
curvilinear  motion  arises. 
Let  there  be  placed  upon  a 
table  a  ball,  A,  and  from  the 
top  of  the  room,  by  a  long 
thread,  let  there  be  suspend- 
ed a  second  ball,  B,  the  point 
of  suspension  being  verti- 
cally over  A.  If  now  we  re- 
move B  a  short  distance 
from  A,  and  let  it  go,  it  falls 
at  once  on  A,  as  though  it 
were  attracted.  It  may  be 
regarded,  therefore,  as  under 
the  influence  of  a  centripetal  force  emanating  from  A. 


Pig.  107. 


What  must  the  nature  of  the  two  forces  be  ?  What  is  the  center  of 
gravity  ?  What  is  the  centripetal  force  ?  What  is  the  tangential  force  ? 
Describe  the  experiment  illustrated  in' Fig.  107. 


CURVILINEAR    MOTIONS. 


97 


But  if,  instead  of  simply  letting  B  drop  upon  A,  we  give 
it  an  impulse  in  a  direction  at  right  angles  to  the  line  ir 
which  it  would  have  fallen,  it  at  once  pursues  a  curvilin- 
ear path,  and  may  be  made  to  describe  a  circle  or  an  el- 
lipse according  to  the  relative  intensity  of  the  tangential 
force  given  it. 

This  revolving  ball  imitates  the  motion  of  the  planetary 
bodies  round  the  sun. 

To  understand  how  these  curvilinear  motions  arise,  let 
C  be  the  center  of  gravity,  and  sup- 
pose a  body  at  the  point  a.  Let  a  tan- 
gential force  act  on  it  in  such  a  man- 
ner as  to  drive  it  from  a  to  b,  in  the 
same  time  as  it  would  have  fallen  from 
a  to  d.  By  the  parallelogram  offerees  » 
it  will  move  tof.  When  at  this  point, 
ft  its  inertia  would  tend  to  carry  it  in 
the  directiony^-,  a  distan-ce  equal  to  a 
ft  in  a  time  equal  to  that  occupied  in 
passing  from  a  tof;  but  the  constant 
attractive  force  still  operating  tends  to 
bring  it  to  h;  by  the  parallelogram  of 
forces  it  therefore  is  carried  to  k  ;  and 
by  similar  reasoning  we  might  show 
that  it  will  next  be  found  at  n,  and  so  on.  But  when  we 
consider  that  the  centripetal  force  acts  continually,  and 
not  by  small  interrupted  impulses,  it  is  obvious  that,  in- 
stead of  a  crooked  line,  the  path  which  the  body  pursues 
will  be  a  continuous  curve. 

The  planets  move  in  their  orbits  round  the  sun,  and 
the  satellites  round  their  planets,  in  consequence  of  the 
action  of  two  forces — a  centripetal  force,  which  is  gravi- 
tation, and  a  tangential  force  originally  impressed  on  them. 

The  centrifugal  force  obviously  arises  from  the  action 
of  the  tangential.  It  is  the  antagonist  of  the  centripetal 
force. 

The  figure  of  the  curve  in  which  a  body  revolves  is  de- 
termined by  the  relative  intensities  of  the  centripetal  and 
tangential  forces.  If  the  two  be  equal  at  all  points  the 
curve  will  be  a  circle,  and  the  velocity  of  the  body  will 

Explain  why  this  curvilinear  motion  ensues.  What  forces  direct  the 
motions  of  the  planets  ?  What  is  the  relation  between  the  centripetal 
and  centrifugal  force  ? 

E 


98 


CURVILINEAR    MOTIONS. 


be  uniform.  But  if  the  centrifugal  force  at  different 
points  of  the  body's  orbit  be  inversely  as  the  square  of  its 
distance  from  the  center  of  gravity,  the  curve  will  be  an 
ellipse  and  the  velocity  of  the  body  variable. 

In  elliptical  motion,  which  is  the  motion  of  planetary 
bodies,  the  center  of  gravity  is  in  one  of  the  foci  of  the 
ellipse.  All  lines  drawn  from  this  point  to  the  circumfe- 
rence are  called  radii  vectorcs,  and  the  nature  of  the  mo- 
tion is  necessarily  such  that  the  radius  vector  connecting 
the  revolving  body  with  the  center  of  gravity  sweeps  over 
equal  areas  in  equal  times. 

The  squares  of  the  velocities  are  inversely  as  the  dis- 
tances, and  the  squares  of  the  times  of  revolution  are  to 
each  other  as  the  cubes  of  the  distances. 

Fig,  109. 


Let  A  B  D  E  be  an  elliptical  orbit,  as,  for  example,  that 
of  a  planet,  the  longest  diameter  being  A  B,  and  the  short- 
est D  E.  The  points  F  and  G  are  thejbci  of  the  ellipse, 
and  in  one,  as  F,  is  placed  the  center  of  gravity,  which, 
in  this  instance,  is  the  sun.  The  planet,  therefore,  when 
pursuing  its  orbit,  is  much  nearer  to  the  sun  when  at  A 
than  when  at  B.  The  former  point  is,  therefore,  called 
the  perihelion,  the  latter  the  aphelion,  and  D  and  E  points 

By  what  circumstance  is  the  figure  of  the  curve  determined  ?  Under 
what  circumstances  is  it  a  circle  ?  Under  what  an  ellipse  ?  What  is  the 
radius  vector  ?  What  are  the  laws  of  elliptic  motion  ? 


FIGURE    OF    REVOLUTION.  99 

of  mean  distance.  The  line  A  B,  joining  the  perihelion 
and  aphelion,  is  the  line  of  the  apsides  ;  it  is  also  the  great- 
er or  transverse  axis  of  the  orbit,  and  D  E  is  the  conju- 
gate or  less  axis.  A  line  drawn  from  the  center  of  grav- 
ity to  the  points  D  or  E,  as  F  D,  is  the  mean  distance,  F 
is  the  lower  focus,  G  the  higher  focus,  A  the  lower  apsis, 
B  the  higher  apsis,  and  F  C  or  G  C — that  is  the  distance 
of  either  of  the  foci  from  the  center — the  excentricity. 

When  a  body  rotates  upon  an  axis  all  its  parts  revolve 
in  equal  times.  The  velocity  of  each  particle  increases 
with  its  perpendicular  distance  from  the  axis,  and,  there- 
fore, so  also  does  its  centrifugal  force.  As  long  as  this 
force  is  less  than  the  cohesion  of  the  particles,  the  rotating 
body  can  preserve  itself,  but  as  soon  as  the  centrifugal  force 
overcomes  the  cohesive,  the  parts  of  the  rotating  mass  fly  off 
in  directions  which  are  tangents  to  their  circular  motion. 

There  are  many  familiar  instances  which  are  examples 
of  these  principles.  The  bursting  of  rapidly  rotating 
masses,  the  expulsion  of  water  from  a  mop,  the  projec- 
tion of  a  stone  from  a  sling. 

If  the  parts  of  a  rotating  body  have  freedom  of  motion 
among  themselves,  a  change  in  the  figure  of  that  body 
may  ensue  by  reason  of  the  difference  of  centrifugal  force 
of  the  different  parts.  Thus,  in  the  case  of  the  earth,  the 
figure  is  not  a  perfect  sphere,  but  a  spheroid,  the  diame- 
ter or  axis  upon  which  it  revolves,  called  its  polar  diam- 
eter, is  less  than  its  equatorial,  it  having  assumed  a  flat- 
tened shape  toward  the  poles  and  a  bulging  one  toward 
the  equator.  At  the  equator  the  centrifugal  force  of  a 
particle  is  ¥L_  of  its  gravity.  This 
diminishes  as  we  approach  the 
poles,  where  it  becomes  0.  The 
tendency  to  fly  from  the  axis  of 
motion  has,  therefore,  given  rise 
to  the  force  in  question. 

In  Fig.  110,  we  have  a  repre- 
sentation of  the  general  figure  of 
the  earth,  in  which  N  S  is  the 
polar  diameter  and  also  the  axis 
of  rotation,  E'E,  the  equatorial  diameter. 

Define  the  various  parts  of  an  elliptic  orbit.  Describe  the  phenomena 
of  rotation  on  an  axis.  What  figure  does  a  movable  rotating  mass  tend 
to  assume  ? 


100 


FIGURE    OF    REVOLUTION. 


This  may  be  illustrated  by  an  instrument  represented 
Fig.  in.  in  Fig.  Ill,  which  consists 

of  a  set  of  circular  hoops, 
made  of  brass  or  other  elas- 
tic material.  They  are  fast- 
ened upon  an  axis  at  the  point 
a,  but  at  the  point  b  can  slide 
up  and  down  the  axis.  When 
at  rest  they  are  of  a  circular 
form.  By  a  multiplying- 
wheel  a  rapid  rotation  can 
be  given  them,  and  when  this 
is  done  they  depart  from  the 
circular  shape  and  assume 
an  elliptical  one,  the  shorter 
axis  being  the  axis  of  rotation. 

But  if  the  parts  of  the  rotating  body  have  not  perfect 
Fie.  112.  freedom  of  motion  among  themselves, 

their  centrifugal  force  gives  rise  to  a 
pressure  upon  the  axis.  If  the  mass 
is  symmetrical  as  respects  the  axis,  the 
resulting  pressures  compensate  each 
other.  But  as  each  one  of  the  rotating 
particles,  by  reason  of  its  inertia,  has 
a  disposition  to  continue  its  motion  in 
the  same  plane,  it  is  obvious  that  such 
a  free  axis  can  only  be  disturbed  from 
MBi^iiir.iUiiiMiiiriiiiU'iM  jts  position  by  the  exercise  of  a  force 
sufficient  to  overcome  that  effect.  It  is  this  result  which 
is  so  well  illustrated  by  Bohnenberger's  machine  (Fig. 
112),  already  described. 

What  does  the  instrument,  Fig.  Ill,  illustrate?  Under  what  circum- 
stances does  pressure  on  the  axis  take  place  ?  For  what  reason  does  the 
axis  tend  to  maintain  the  same  direction  ? 


CAPILLARY    ATTRACTION. 


101 


LECTURE  XXII. 

OF  ADHESION  AND  CAPILLARY  ATTRACTION. — Adhesion  of 
Solids  and  Liquids. — Law  of  Wetting. — Capillary  At- 
traction.— Elevations  and  Depressions. — Relations  of  the 
Diameter  of  Tubes. — Motions  by  Capillary  Attraction. — 
Endos7nosis  of  Liquids  and  of  Gases. 

To  the  arm  of  a  balance,  b  c,  Fig.  113,  let  there  be  at- 
tached a  flat  circular  plate  of  glass,  Kg.  113. 
#,  arid  let  it  be  equipoised  by  the 
weights  in  the  opposite  scale,  d; 
beneath  it  let  there  be  brought  a 
cup  of  water,  e,  and  on  lowering  the 
glass  plate  within  an  inch,  or  even 
within  the  hundredth  part  of  an 
inch  of  the  water,  no  attraction  is  exhibited ;  but  if  the 
glass  and  the  water  are  brought  in  contact,  then  it  will  re- 
quire the  addition  of  many  weights  in  the  opposite  scale 
to  pull  them  apart. 

If  the  cup,  instead  of  being  filled  with  water,  is  filled 
with  quicksilver,  alcohol,  oil,  or  any  other  liquid,  or  if 
instead  of  a  plate  of  glass  we  use  one  of  wood  or  metal, 
the  same  effects  still  ensue.  The  force  which  thus  main- 
tains the  surface  in  contact  is  called  "  Adhesion." 

Adhesion  does  not  alone  take  place  between  bodies  of 
different  forms.  Two  perfectly  flat  plates  of  glass  or  mar- 
ble, when  pressed  together,  can'  only  be  separated  by  the 
exertion  of  considerable  force.  In  both  this  and  the  for- 
mer case  the  absolute  force  required  to  effect  a  separa- 
tion depends  on  the  superficial  area  of  the  bodies  in  con- 
tact. 

If,  on  bringing  a  given  solid  in  contact  with  a  liquid, 
the  force  of  adhesion  is  equal  to  more  than  half  the  co- 
hesive force  of  the  liquid  particles  for  one  another,  the 
liquid  will  adhere  to  the  solid  or  wet  it.  Thus,  the  adhe- 

Give  an  example  of  the  adhesion  of  a  solid  to  a  liquid.  Does  this  take 
place  when  liquids  of  different  kinds  are  used  ?  Does  it  take  place  when 
two  solids  are  employed  ?  Under  what  circumstances  does  a  liquid  wet 
or  not  wet  a  solid  ? 


102 


CAPILLARY    TUBES. 


Fig.  114. 


sive  force  developed  when  gold  is  brought  in  contact  with 
quicksilver  is  more  than  half  the  cohe- 
sion of  the  particles  of  the  quicksilver 
for  each  other  :  the  quicksilver,  there- 
fore, adheres  to  or  wets  the  gold. 

But  if  the  force  of  adhesion  devel- 
oped between  a  solid  and  liquid  is 
less  than  half  the  cohesive  force  of  the 
particles  of  the  latter,  the  liquid  does 
not  wet  the  solid.  Thus,  a  piece  of 
glass  in  contact  with  quicksilver  is  not 
wetted. 

It  is  on  these  principles  that  Vera's 
pump  acts.     It  consists  of  a  cord  which 
passes  over  two  wheels,  to  which  a 
rapid  motion  can  be  given.     The  water 
adheres  to  the  cord  and  is  raised  by  it. 

If  the  surface  of  some  water  be  dusted  over  with  lyco- 
podium  seeds,  the  fingers  may  be  plunged  in  it  without 
being  wetted,  the  lycopodium  preventing  any  adhesion 
of  the  water. 

But  it  is  in  the  phenomena  of  capillary  attrac- 
tion that  we  see  the  effects  of  adhesion  in  the 
most  striking  manner.  These  phe- 
nomena are  exhibited  by  tubes  of 
small  diameter,  called  capillary  tubes, 
because  their  bore  is  as  fine  as  a 
hair.  If  such  a  tube,  a,  Fig.  115,  be 
immersed  in  water,  the  water  at  once 
rises  in  it  to  a  height  considerably  above  its 
level,  in  the  glass  cup,  b.  - 

Or  if  instead  of  water  we  fill  the  glass  cup 
with  quicksilver,  and  immerse  the  tube  in  it, 
bringing  it  near  the  side  so  that  we  can  see  the 
metal  in  the  interior  of  the  tube  through  the 
glass,  it  will  be  found  to  be  depressed  be- 
neath its  proper  level. 

These  experiments  are  still  more  conve- 
niently  made  by  means  of  tubes  bent  in  the 
form  of  a  syphon,  as  represented  in  Fig.  116. 
If  one  of  these,  A  I,  be  partially  filled  with  water,  and 


Fig.  115. 


Fig.  116. 


What  is  the  principle  of  the  action  of  Vera's  pump  ? 
lary  tube  ?    What  phenomenon  do  these  tubes  exhibit  ? 


What  is  a  capil- 


SURFACE   OF    LIQUIDS.  103 

then  with  quicksilver,  the  water  will  be  seen  to  rise  in  the 
narrow  tube,  G  D,  above  its  level  in  the  wide  tube,  A  I, 
and  the  quicksilver  to  be  depressed. 

When  tubes  of  different  diameters  are  used,  the  change 
in  the  level  of  the  liquid  is  different.  The  narrower  the 
tube  the  higher  will  water  rise,  and  the  lower  will  quick- 
silver be  depressed. 

When  tubes  are  very  wide,  or,  what  comes  to  the  same 
thins:,  when  liquids  are  contained  in 

i  f  •       f          i  Fig.  117. 

bowls  or  basins,  the  surface  is  found  not 
to  be  uniformly  level ;  but  near  those 
points  where  it  approaches  the  glass,  in 
the  case  of  water,  it  curves  upward  as 
seen  at  A,  Fig.  117,  and  in  the  case  of 
quicksilver  it  curves  downward  as  seen 
atB. 

In  tubes  of  the  same  material  dipped  in  the  same 
liquid,  the  elevations  or  depressions  are  inversely  as  the 
diameters  of  the  tubes,  the  narrower  the  tube  the  higher 
will  water  rise,  and  the  deeper  will  quicksilver  be  de- 
pressed. 

There  is  a  beautiful  experiment  which  shows  the  con- 
nection between  the  diameter  of 
the  tube  and  the  height  to  which 
it  will  lift  a  liquid.  Two  square 
pieces  of  plate  glass,  A  B,  C  D, 
Fig.  118,  are  arranged  so  that 
their  surfaces  form  a  minute  an- 
gle. This  position  may  be  easily- 
given  them  by  fastening  them  to- 
gether with  a  piece  of  wax  or 
cement,  K.  When  the  plates  are  dipped  into  a  trough 
of  water,  E  F,  G  H,  the  water  rises  in  the  space  between 
them  to  a  smaller  extent  where  the  plates  are  far  apart, 
and  to  a  greater  where  they  are  closer.  The  upper  edge 
of  the  water  gives  the  form  of  a  hyperbola,  D  I  A.  The 
plates  may  be  supposed  to  represent  a  series  o'f  capillary 
tubes  of  diameters  continually  decreasing,  they  show  that 
the  narrower  the  intercluded  space  or  bore  of  such  tubes 
the  higher  the  liquid  will  rise. 

The  figure  of  the  surface  which  bounds  a  liquid  in  a 

Does  this  depend  on  the  width  of  the  tube  ?  How  does  the  experiment 
of  Fig.  118  illustrate  this? 


104 


CAPILLARY    MOTIONS. 


Fiff  119.  capillary  tube  is  also  to  be  remarked. 

Whenever  a  liquid  rises  in  a  tube,  its 
bounding  surface  is  concave  upward, 
^  as  seen  in  Fig.  119,  where  fg  is  the 
tube,  and  a  a  the  surface.  When  the 
liquid  neither  rises  nor  sinks,  the  sur- 
face a  a  is  plane,  as  at  d  e;  when  the 
liquid  is  depressed,  the  surface  a  a  is 
convex  upward,  as  seen  at  b  c.  All 
these  conditions  may  be  exhibited  by 
a  glass  tube  properly  prepared.  In  such  a  tube,  when 
quite  clean,  the  concavity  and  elevation  of  the  liquid  is 
seen ;  if  the  interior  of  the  tube  be  slightly  greased,  the 
surface  of  the  water  in  it  is  plane,  and  it  coincides  in 
position  with  the  level  on  the  exterior.  If  it  be  not  only 
greased,  but  also  dusted  with  lycopodium,  the  liquid  is 
depressed  in  it,  and  has  a  convex  figure. 

Jt  may  be  shown,  according  to  the  principles  of  hydro- 
statics, that  it  is  the  assumption  of  this  curved  surface 
which  is  the  cause  of  the  elevation  or  depression  of  liquids 
in  capillary  tubes. 

Motions  often  ensue  among  floating  bodies  in  conse- 
quence of  capillary  attraction.  At 
first  sight  they  might  seem  to  indi- 
cate the  exertion  of  direct  forces 
of  attraction  and  repulsion  ema- 
nating from  the  bodies  themselves ; 
but  this  in  reality  is  not  the  case, 
the  motions  arising  in  consequence 
of  a  disturbance  of  the  figure  of  the 
surface  on  which  the  bodies  float.  Thus,  if  we  grease 
two  cork  balls,  A  B,  and  dust  them  with  lycopodium 
powder,  they  will,  when  set  upon  water,  repel  the  liquid 
all  round,  each  ball  reposing  in  a  hollow  space.  If  brought 
iieac  to  each  other,  their  repulsion  exerted  on  the  water 
a*  G  makes  a  complete  depression,  and  they  fall  toward 
one  another  as  though  they  were  attracting  each  other. 
It  is,  however,  the  lateral  pressure  of  the  water  beyond 
which  forces  them  together. 

Under  what  circumstances  is  the  boundary  surface  concave,  plane,  and 
convex  ?  What  is  it  that  determines  the  elevation  or  depression  of  the 
liquid  ?  Describe  the  motions  which  take  place  in  floating  bodies  in  con- 
sequence of  these  facts. 


ENDOSMOSIS.  105 

Again,  if  one  of  the  balls,  E,  is  greased  and  dusted  with 
lycopodium,  arid  the  other,  D,  clean,  and  therefore  capa- 
ble of  being  moistened,  an  elevation  will  exist  all  round 
D,  and  a  depression  round  E.  When  placed  near  to- 
gether the  balls  appear  to  repel  each  other,  the  action 
in  this  case,  as  in  the  former,  arising  from  the  figure  of 
the  surface  of  the  water. 

If  we  take  a  small  bladder,  or  any  other  membranous 
Fig.  121.       cavity,  and   having  fastened   it   on    a   tube 
open  at  both  ends,  A  B,  Fig.  12],  fill  the 
bladder  and  tube  to  the  height,  C,  with  alco- 
hol, and  then  immerse  the  bladder  in  a  large 
vessel  of  water  ;  it  will  soon  be  seen  that  the 
level  at  C  is  rising,  and  at  a  short  time  it 
reaches  the  top  of  the  tube  at  B,  and  over- 
flows. This  motion  is  evidently  due  to  the  cir- 
cumstance that  the  water  percolates  through 
the  bladder,  and  the  phenomenon  has  some- 
times  been    called  endosmosis,    or    inward 
movement.     Examination  proves  that  while 
the  water  is  thus  flowing  to  the  interior,  a  little  of  the  al- 
cohol is  moving  in  the  opposite  way  ;  but  as  the  water 
moves  quicker  than  the  alcohol,  there  is  an  accumulation 
in  the  interior  of  the  bladder,  and,  consequently,  a  rise  at  C. 
One   liquid  will  thus   intrude  itself  into  another  with 
very  great  force.     A  bladder  filled  full  of  alcohol,  and  its 
neck  tightly  tied,  will  soon  burst  open  if  it  be  plunged 
beneath  water. 

Similar  phenomena  are  exhibited  by  gases.     If  a  jar 
Fig.  122.  De  filled  with  carbonic  acid  gas,  and  a 

piece  of  thin  India-rubber  tied  over  it, 
the  carbonic  acid   escapes  into  the  air 
through  the  India-rubber,  which  becomes 
deeply  depressed  as  at  A,  Fig.  122.   But 
if  the  jar  be  filled  with  air,  and  be  ex- 
posed to  an  atmosphere  of  carbonic  aciu, 
this  gas,  passing  rapidly  through  it,  ac- 
cumulates in  the  interior  of  the  vessel,  and  gives  to  the 
India-rubber  a  convex  or  dome-shaped  form,  as  seen  at  B. 
Endosmosis  is  nothing  but  a  complex  case  of  common 
capillary  attraction. 

Under  what  circumstances  does  repulsion  take  place?  What  is  meant  by 
endosinosis  ?  Do  gases  exhibit  these  properties  ?  Give  an  illustration  of  it. 


106  RISE    OF    SAP. 

The  facts  here  described  were  originally  discovered  by 
Priestley ;  but  at  a  later  period  attention  was  called  to 
them  by  Dutrochet,  who,  regarding  them  as  being  due  to 
a  peculiar  physical  principle,  gave  to  the  movements  in 
question  the  names  of  endosmose  and  exosmose,  mean- 
ing inward  and  outward  motion.  But  I  have  shown  that 
there  is  no  reason  to  revert  to  any  peculiar  physical  prin- 
ciple, since  the  laws  of  ordinary  capillary  attraction  ex- 
plain every  one  of  the  facts. 

The  bursting  of  a  bladder  rilled  with  alcohol  and  sunk 
under  water  gives  us  some  idea  of  the  power  with  which 
the  latter  liquid  forces  its  way  into  the  membranous 
cavity  ;  and  it  is  surprising  with  what  a  degree  of  energy 
these  movements  are  often  accomplished.  An  opposing 
pressure  of  two  or  three  atmospheres  seems  to  offer  no 
obstacle  whatever,  and  I  have  seen  gases  pass  through 
India-rubber  to  mingle  with  each  other,  though  resisted 
by  pressures  of  from  twenty  to  fifty  atmospheres. 

Whenever  liquids  which  can  commingle  are  placed  on 
opposite  sides  of  a  membrane  or  cellular  body  which 
they  can  wet,  motion  ensues  ;  both  liquids  simultaneously 
moving  in  opposite  directions,  and  commonly  one  much 
faster  than  the  other.  Thus,  if  a  bladder  full  of  gum- 
water  is  immersed  in  common  water,  the  latter  will  find 
its  way  into  the  former  against  any  pressure  whatever. 

During  the  growth  of  trees,  the  terminations  of  their 
roots,  which  are  of  a  soft  and  succulent  nature,  and  which 
pass  under  the  name  of  spongioles,  are  filled  with  a  gummy 
material  which  originally  was  formed  in  the  leaves.  The 
moist  or  wet  soil  with  which  the  spongioles  are  in  contact, 
continually  furnishes  a  supply  of  water  which  enters  those 
organs  in  precisely  the  same  way  that  it  would  enter  a 
bladder  full  of  gum-water.  An  accumulation  takes  place 
in  the  organs,  and  the  liquid  rises  in  the  vascular  parts  of 
the  root  and  the  stem,  which  are  in  connection  therewith. 
To  this  we  give  the  name  of  ascending  sap.  It  makes  its 
way  to  the  leaves,  there  to  be  changed  into  gum-water  by 
the  action  of  the  light  of  the  sun.  It  is  immaterial  how 
hig-l\a  tree  may  be,  the  force  now  under  consideration  is 
competent  to  lift  the  sap  to  any  altitude. 

With  what  degree  of  force  are  these  motions  accomplished  ?   What  is 
the  cause  of  the  rise  of  the  sap  ? 


PROPERTIES    OF    SOLIDS.  107 


PROPERTIES  OF  SOLIDS. 


LECTURE  XXIII. 

GENERAL  PROPERTIES  OF  SOLIDS. — Distinctive  Properties. 
— Changes  by  particular  Processes. — Absolute  Strength. 
— Lateral  Strength. — Resistance  to  Compression. —  Tor- 
sion.—  Torsion  Balance. 

A  SUBSTANCE  which  can  of  itself  maintain  an  independ- 
ent figure  has  already  been  defined  as  a  solid  body.  This 
peculiarity  arises  from  the  relative  intensity  of  the  attract- 
ive and  repulsive  forces  which  obtain  among  its  particles. 
In  solids  the  attractive  predominates  over  the  repulsive 
force ;  in  liquids  there  seems  to  be  little  difference  in  their 
intensity ;  in  gases  the  repulsive  force  prevails.  It  is  fur- 
ther to  be  observed,  that  portions  of  gas  uniformly  mix 
with  each  other;  the  same  also  takes  place  with  liquids 
of  a  similar  kind ;  but  when  a  fragment  is  broken  from  a 
solid  mass  mere  coaptation  will  not  effect  reunion. 

The  cohesive  force  of  solids  is  exhibited  in  very  dif- 
ferent degrees — some  solids  being  brittle,  and  some  duc- 
tile— some  are  hard,  and  others  soft.  Thus  glass  and 
bismuth  may  be  pulverized  in  a  mortar;  but  gold  can  be 
beaten  out  to  an  incredible  extent  by  a  hammer,  and  cop- 
per drawn  into  fine  wires.  The  diamond  is  the  hardest 
of  all  substances  known,  and,  from  their  possessing  the 
same  quality,  rhodium  and  indium  are  used  for  the  tips 
of  metallic  pens,  while  other  solids,  such  as  potassium,  so- 
dium, butter,  are  soft,  and  yield  to  a  very  moderate  press- 
ure. 

Mention  some  of  the  peculiarities  of  solid  bodies.  Give  examples  of 
brktleness,  hardness,  and  softness. 


108  STRENGTH    OF    MATERIALS. 

It  has  already  been  stated  that  the  special  properties 
which  bodies  possess  can  often  be  changed  by  proper 
processes.  Thus  glass,  by  slow  cooling,  loses  much  of 
its  brittleness;  and  steel  may  be  made  excessively  hard  by 
being  ignited  and  then  plunged  in  cold  water.  Prince 
Rupert's  drops  furnish  an  illustration  of  these  effects  ; 
they  are  made  by  suffering  drops  of  melted  glass  to  fall 
in  water.  The  drop  takes  on  a  pear-shaped  form,  ter- 
minating in  a  long  thread.  It  will  stand  a  tolerably  heavy 
blow  on  the  thick  part,  but  bursts  to  dust  if  the  tip  of  the 
thin  part  is  broken. 

Solid  substances  differ  very  much  in  the  important  pecu- 
liarity of  STRENGTH.  Of  all  bodies  steel  is  the  strongest. 
The  strength  of  materials  may  be  considered  in  four 
ways  :  — 

1st.  Absolute  strength,  or  the  resistance  exerted  against 
a  force  tending  to  tear  asunder. 

2d.  Lateral  or  respective  strength  —  the  resistance  ex- 
erted against  being  broken  across. 

3d.  Resistance  to  compression  —  that  is  to  a  force  tend- 
ing to  crush. 

4th.  Strength  of  torsion  —  the  resistance  against  separa- 
tion by  being  twisted. 

The  absolute  strength  of  a  body  may  be  determined  by 
fastening  its  upper  end  and  attaching  weights  to  the  lower 
till  it  breaks.  The  absolute  strength  is  not  affected  by* 
the  length  of  a  body,  but  is  proportional  to  the  area  of 
its  section.  A  rod  of  tempered  steel,  the  area  of  which 
is  one  inch,  requires  nearly  115,000  Ibs.  to  tear  it  asunder. 
The  strength  of  cords  depends  on  the  fineness  of  the 
strands  ;  damp  cordage  is  stronger  than  dry.  Silk  cords, 
of  the  same  diameter,  have  thrice  the  strength  of  those 
of  flax,  and  a  remarkable  increase  of  power  arises  from 
gluing  the  threads  together.  A  hempen  cord,  the 
threads  of  which  are  glued,  is  stronger  than  the  best 
wrought-iron. 

The  lateral  strength  of  a  beam  of  the  shape  of  a  paral- 
lelopipedon  and  of  uniform  thickness,  supported  at  its 


Can  these  properties  be  changed?  What  phenomenon  do  Prince  Ru- 
pert s  drops  exhibit  ?  What  is  meant  by  absolute  strength?  What  by 
lateral  ?  What  by  resistance  to  compression  ?  What  by  torsion  ?  How 
may  absolute  strength  be  determined  ?  Upon  what  does  it  depend  ?  What 
is  the  law  of  lateral  strength  of  rectangular  beams  ? 


TORSION. 


109 


ends  and  loaded  in  the  middle,  is  inversely  as  the  length 
and  directly  as  the  product  of  the  breadth  into  square  of 
the  depth.  This  strength  is  least  when  the  whole  weight 
acts  at  the  middle,  and  is  greatest  when  at  the  ends. 

The  resistance  to  compression  increases  as  the  section 
of  the  body  increases,  and  it  diminishes  as  the  body  be- 
comes longer.  When  the  body  is  only  a  thin  plate,  its 
resistance  to  compression  is,  however,  very  small ;  but  it 
rapidly  increases  with  increasing  thickness — reaches  a 
maximum,  and  then  diminishes  as  the  square  of  the  length. 
This  species  of  resistance  is  called  into  operation  in  the 
construction  of  pillars  or  columns. 

Torsion  resistance  is  connected  with  the  elasticity  of  a 
body.  As  respects  this  force,  elasticity,  we  have  already 
defined  it,  and  shown  that  no  solid  substance  is  perfectly 
elastic,  though  gases  are.  Each  solid  has  its  own  limit 
of  elasticity,  beyond  which,  if  it  be  strained,  it  takes  a 
permanent  set  or  it  breaks.  The  limit  of  elasticity  of  glass 
is  the  point  at  which  it  breaks,  and  that  of  iron  or  copper 
being  reached,  the  metal  takes  a  permanent  set. 

The  resistance  arising  from  elasticity  is  proportional  to 
the  displacement  of  the  particles  of  the  elastic  body. 

The  application  of  this  law  is  in- 
volved in  several  valuable  philosoph- 
ical instruments,  among  which  may 
be  mentioned  the  torsion  balance, 
used  for  the  determination  of  weak 
electric  or  magnetic  forces. 

THE  TORSION  BALANCE  consists  of 
a  delicate  thread  of  glass  or  other 
highly  elastic  substance,  a  b,  Fig. 
123,  fastened  at  its  upper  end,  a,  to 
a  button,  which  turns  stiffly  in  the 
graduated  plate,  c,  and  to  its  lower 
end  at  b,  a  lever,  b  d,  is  affixed  trans- 
versely. The  thread  is  inclosed  in 
a  glass  tube,  B,  and  the  transverse 
lever  moves  in  a  glass  cylinder,  A. 
It  is  thus  protected  from  the  dis- 
turbance of  currents  of  air.  Round  this  cylinder,  from 


Fig.  123. 


What  is  the  law  for  resistance  to  compression  ?  With  what  property 
is  torsion  connected  ?  What  is  the  law  of  resistance  by  elasticity  ?  De- 
scribe the  torsion  balance. 


110  CENTER    OF    GRAVITY. 

0   to  180,  graduated  divisions  are  marked,  and  the  whole 
instrument  can  be  leveled  by  means  of  screwsyyi 

Suppose,  now,  it  were  required  to  measure  any  feeble 
repulsive  force  as  the  repulsion  of  a  little  electrified  ball,  e. 
If  this  ball  be  introduced  into  the  interior  of  the  cylinder 
through  an  aperture  in  the  top,  as  shown  in  the  Fig.  123, 
the  index  at  c  and  the  ball  at  d  being  both  at  the  zero  of 
their  respective  scales,  the  repulsion  of  e  will  drive  the 
movable  ball  d  through  a  certain  number  of  degrees. 
By  twisting  the  button  at  a,  we  can  compel  d  to  go  back 
to  its  original  position  ;  and  the  number  of  degrees  through 
which  the  thread  must  be  twisted  to  effect  this,  measures 
the  repulsive  force  for  the  angle  of  torsion  is  always  pro- 
portional to  the  force  exerted.  Of  all  methods  for  determ- 
ining feeble  forces  in  a  horizontal  plane,  the  torsion 
balance  is  the  most  delicate  and  accurate. 


LECTURE  XXIV. 

THE  CENTER  OF  GRAVITY. — Definition  of  the  Center  of 
Gravity. — Line  of  Direction. — Position  of  Equilibrium. 
—  Three  Conditions  of  Support. — Resulting  States  of 
Equilibrium. — Stability  of  Bodies. —  The  Floating  of 
Bodies. 

IN  every  solid  body  there  exists  a  certain  point  round 
which  its  material  particles  are  arranged  so  as  to  be 
equally  acted  on  by  gravity.  The  gravitating  forces 
soliciting  these  particles  may  be  regarded  as  acting  in 
lines  which  are  parallel  to  one  another ;  for  the  common 
point  of  attraction,  the  center  of  the  earth,  is  so  distant, 
that  lines,  drawn  from  it  to  the  different  particles  of  any 
body  on  its  surface,  are  practically  parallel.  To  this 
point,  thus  found  in  every  body,  no  matter  what  may  be 
its  figure  or  density,  the  term  "  Center  of  Gravity"  is 
applied. 

A  line  which  connects  the  center  of  gravity  with  the 
centre  of  the  earth  (or,  what  is  the  same  thing,  a  line 

What  is  meant  by  the  center  of  gravity  of  bodies  ? 


CONDITIONS    OF    SUPPORT.  Ill 

drawn  from  the  center  of  gravity  perpendicularly  down- 
ward) is  called  "  the  line  of  direction."  If  a  solid  be  suf- 
fered to  fall,  its  center  of  gravity  moves  along  the  line  of 
direction  until  it  reaches  the  ground. 

In  our  reasonings  in  relation  to  solids,  we  may  regard 
them  as  if  all  their  material  particles  were  concentrated 
in  one  point — that  point  being  the  center  of  gravity—- 
this being  the  point  of  application  of  the  earth's  attraction. 
It  follows,  therefore,  that  if  a  body  has  freedom  of  motion, 
it  cannot  be  brought  into  a  position  of  permanent  equilib- 
rium until  the  center  of  gravity  is  at  the  lowest  place. 

To  satisfy  this  condition,  sometimes  effects  which  are 
apparently  contradicto- 
tory  will  ensue.  Thus, 
the  cylinder,  m,  Fig. 
124,  so  constructed,  by 
being  weighted  on  one 
side,  as  to  have  its  cen- 
tre of  gravity  at  the 
point  g,  while  its  ge- 
ometrical  center  is  at  c,  will  roll  up  an  inclined  plane,  A 
B,  continuing  its  motion  until,  as  shown  at  m't  where  the 
center  of  gravity,  g',  is  in  the  lowest  position. 

A  prop  which  supports  the  center  of  gravity  of  a  body 
supports  the  whole  body.  There  are  three  different  po- 
sitions in  which  this  support  may  be  given  : — 

1st.  The  prop  may  be  applied  directly  to  the  center 
itself. 

2d.  The  point  of  support  may  have  the  center  imme- 
diately below  it. 

3d.  The  point  of  support  may  have  the  center  imme- 
diately above  it. 

In  the  first  case,  when  the  point  of  support  is  directly 
applied  to  the  center  of  gravity  itself,  the  body,  whatever 
its  figure  may  be,  will  remain  at  rest  in  any  position — as 
is  the  case  in  a  common  wheel,  the  center  of  gravity  of 
which  is  in  the  center  of  its  figure,  and  this  being  sup- 
ported upon  the  axle,  the  wheel  rests  indifferently  in  any 
position. 

Let  b  a  d,  Fig.  125,  be  a  brass  semi-circle,  weighted 

What  is  the  line  of  direction  ?  What  is  the  position  of  equilibrium  of 
the  center  of  gravity  ?  In  what  three  positions  may  the  center  of  gravity 
be  supported  ?  What  phenomena  arise  in  the  first  position  ? 


112 


SUPPORT    OF    BODIES. 


Fig.  125.  at  the   parts  &  d  to  such  an  extent 

that  the  center  of  gravity  falls  upon 
the  line  connecting  b  and  d.  To  a 
fasten  a  light  arm,  a  c,  long  enough 
to  reach  to  that  line,  and  on  this 
arm,  as  shown  by  the  figure,  the 
whole  body  may  be  balanced. 

2d.  The  point  of  support  may  be 
above  the   center    of  gravity.     In 
this  case,  if  the  body  have  freedom 
of  motion,  it  will  not  rest  in  equi- 
librio  until  its  center  of  gravity  has 
descended    to  the  lowest  position 
possible,  or  until  it  is  perpendicularly  beneath  the  point  of 
Fig.  126.         suspension.     Thus,  let  there  be  a  circular 
plate,  E  c,  Fig.  126,  the  center  of  gravity 
of  which  is  at  c,  and  let  it  be  suspended  at 
the  point  E,  having  freedom  of  motion  on 
that   point.     Whatever   position   we   may 
give  it  to  the  right  or  left,  as  shown  by  the 
dotted  lines,  it  at  once  moves,  and  is  only  at  rest  when  E 
and  c  are  in  the  same  perpendicular  line. 

In  the  same  manner,  if  a  ball  be  suspended  to  a  point 
by  a  thread,  whatever  position  may  be  given  it,  there  is 
but  one  in  which  it  will  remain  at  rest,  and  that  is  when 
its  center  of  gravity  is  immediately  beneath  the  point  of 
suspension,  and  the  thread  in  a  vertical  line. 

3d.  The  point  of  support  may  be  beneath  the  center 
of  gravity.  In  this  case,  also,  the  body  will  be  in  equilib- 
rio  and  at  rest ;  but  the  nature  of  its  equilibrium  differs 
essentially  from  that  of  the  foregoing  case,  as  we  shall 
presently  see.  A  sphere  upon  a  horizontal  plane  affords 
a  case  in  point;  and,  as  its  center  of  gravity  is  also  its 
center  of  figure,  it  will  be  at  rest,  no  matter  what  may 
be  the  particular  point  of  its  surface  to  which  the  support 
is  applied. 

Upon  the  principle  that  if  a  body  be  suspended  freely, 
and  a  perpendicular  be  drawn  from  the  point  of  suspen- 
sion, it  will  pass  through  the  center  of  gravity,  we  are 

What  does  the  experiment  in  Fig.  125  prove?  In  the  second  position 
of  support  what  are  the  resulting  phenomena  ?  What  are  those  of  the 
third  case  of  support  ?  How  may  the  center  of  gravity  of  plane  bodies  bo 
determined  ? 


STABILITY    OF    BODIES.  113 

often  enabled  to  determine  the  posi-  ffy.  127. 

tion  of  that  center  experimentally. 
Thus,  let  the  plane  body,  ABC,  Fig. 
127,  be  supported  by  a  thread  attach- 
ed to  the  point  A,  and  to  the  same 
point  let  there  be  attached  a  plumb- 
line  :  this  line,  because  it  is  perpen- 
dicular, will  pass  through  the  center 
of  gravity ;  let  the  line  A  m,  against 
which  the  plumb-line  hangs,  be  marked 
upon  the  body.  Next,  let  it  be  suspended,  in  like  man- 
ner, by  another  point,  B,  to  which  the  plumb-line  is  also 
attached;  the  direction,  B  m',  of  the  plumb-line  will,  in 
this  case,  intersect  its  direction  in  the  former  case  at  some 
point,  such  as  G.  This  will  be  the  center  of  gravity. 

When  the  center  of  gravity  is  above  the  point  of  sus- 
pension, there  is  produced  a  pressure  upon  that  point. 
When  the  center  of  gravity  is  beneath  the  point  of  sus- 
pension, there  is  produced  a  pull  upon  that  point. 

The  stability  of  bodies  is  intimately  connected  writh  the 
position  of  their  center  of  gravity.  A  body  may  be  in  a 
condition,  1st,  of  indifferent ;  2d,  of  stable  ;  3d,  of  insta- 
ble  equilibrium. 

Indifferent  equilibrium  ensues  when  a  body  is  support- 
ed upon  its  center  of  gravity  ;  for  then  it  is  immaterial 
what  position  is  given  to  it — it  remains  in  all  at  rest. 

Stable  equilibrium  ensues  when  the  point  of  support  is 
above  the  center  of  gravity.  If  the  body  be  disturbed 
from  this  situation,  it  oscillates  for  a  time,  and  finally  re- 
turns to  its  original  position. 

Instable  equilibrium  is  exhibited  when  the  point  of 
support  is  beneath  the  center  of  gravity.  The  body  being 
movable,  in  this  instance,  it  revolves  upon  its  point  of 
support,  and  turns  into  such  a  position  that  its  center  of 
gravity  comes  immediately  beneath  that  point. 

In  the  theory  of  the  balance,  hereafter  to  be  described, 
these  facts  are  of  the  greatest  importance. 

When  bodies  are  supported  upon  a  basis,  their  stability 
depends  on  the  position  of  their  line  of  direction.  The 

In  what  case  does  a  pressure  and  in  what  a  pull  upon  the  point  of  sus- 
pension arise?  How  many  kinds  of  equilibrium  may  be  enumerated? 
tinder  what  circumstances  do  these  arise?  On  what  does  the  stability  of 
bodies  depend  ? 


114 


STABILITY    OF    BODIES. 


line  of  direction  has  already  been  defined  to  be  a  line 
drawn  from  the  center  of  gravity  perpendicularly  down- 
ward. 

If  the  line  of  direction  falls  within  the  basis  of  support, 
the  body  remains  supported. 

- 128.  If  the.  line  of  direction  falls  out- 

side the  basis  of  support,  the  body 
overturns. 

Thus,  let  there  be  a  block  of 
wood  or  metal,  Fig.  128,  of  which 
c  is  the  center  of  gravity,  c  d  the 
line  of  direction,  and  let  it  be  sup- 
ported on  its  lower  face,  a  b.  So 
long  as  the  line  of  direction  falls  within  this  basis,  the 
block  remains  in  equilibrio. 

Fig.  129.  Again,  let  there  be  another  block, 

Fig.  129,  of  which  c  is  the  center  of 
gravity  and  c  d  the  line  of  direction. 
Inasmuch  as  this  falls  outside  of  the 
basis,  a  b,  the  body  overturns. 

A  ball  upon  a  horizontal  plane  has 
its  line  of  direction  within  its  point  of 
support;  it  therefore  rests  indifferently 
in  any  position  in  which  it  may  be  laid. 
But  a  ball  upon  an  inclined  plane  has 
its  line  of  direction  outside  its  point  of  support,  and  there- 
fore it  falls  continually. 

From  similar  considerations  we  understand  the  nature 
of  the  difficulty  of  poising  a  needle  upon  its  point.     The 


Fig.  J30. 


center  of  gravity  is  above 
the  point  of  support,  and  it 
is  almost  impossible  to  ad- 
just things  so  that  the  line 
of  direction  will  fall  within 
the  basis.  The  slightest  in- 
clination instantly  causes  it 
to  overturn. 

When  the  center  of  grav- 
ity is  very  low,  or  near  the 


What  is  the  condition  for  support,  and  what  for  being  overturned  ?  Illus- 
trate these  cases  in  the  instance  of  square  and  round  blocks.  Why  is  it  so 
difficult  to  poise  a  needle  on  its  point  ?  In  what  circumstances  is  the 
maximum  stability  obtained  ? 


EaUILIBRIUM   IN    FLOTATION.  115 

basis,  there  is  more  difficulty  in  throwing  the  line  of 
direction  outside  the  basis  than  when  it  is  high.  For  this 
reason  carriages,  which  are  loaded  very  high,  or  have 
much  weight  on  the  top,  are  more  easily  overturned  than 
those  the  load  of  which  is  low,  and  the  weight  arranged 
beneath,  as  is  shown  in  Fig.  130. 

The  stability  of  a  body  is  greater  according  as  its 
weight  is  greater,  its  center  of  gravity  lower,  and  its  basis 
wider. 

The  principles  here  laid  down  apply  to  the  case  of  the 
flotation  of  bodies.  When  an  irregular-shaped  solid  mass 
is  placed  on  the  surface  of  a  fluid,  it  arranges  itself  in  a 
certain  position  to  which  it  will  always  return  if  it  be 
purposely  overset.  In  many  such  solids  another  position 
may  be  found,  in  which  they  will  float  in  the  liquid ; 
but  the  slightest  touch  overturns  them.  Bodies,  there- 
fore, may  exhibit  either  stable  or  unstable  flotation.  A 
long  cylinder  floating  on  one  end  is  an  instance  of  the 
.latter  case,  but  if  floating  with  its  axis  parallel  to  the  sur- 
face of  the  liquid,  of  the  former. 

These  phenomena  depend  on  the  relative  positions  of 
the  center  of  gravity  of  the  floating  solid,  and  that  of  the 
portion  of  liquid  which  it  displaces.  The  former  retains 
an  invariable  position  as  respects  the  solid  mass,  but  the 
latter  shifts  in  the  liquid  as  the  solid  changes  its  place. 

Equilibrium  takes  place  when  the  center  of  gravity  of 
the  floating  body  and  that  of  the  portion  of  liquid  dis- 
placed are  in  the  same  line  of  direction.  If  of  the  two 
the  former  is  undermost,  stable  equilibrium  ensues,  but  if 
it  is  above  the  center  of  gravity  of  the  displaced  liquid, 
unstable  equilibrium  takes  place.  To  this,  however, 
there  is  an  exception — it  arises  when  the  body  floats  on  its 
largest  surface. 

There  are  two  forces  involved  in  the  determination  of 
the  position  of  flotation  :  1st,  the  gravity  of  the  body 
downward;  2d,  the  upward  pressure  of  the  liquid.  The 
former  is  to  be  referred  to  the  center  of  gravity  of  the 
body  itself,  and  the  latter  takes  effect  on  the  center  of 
gravity  of  the  displaced  liquid.  If  these  two  centers  are 

What  is  meant  by  stable  and  unstable  flotation  ?  On  what  do  these 
depend  ?  Under  what  circumstances  does  stable  equilibrium  take  place  ? 
Under  what  unstable  ?  What  forces  are  involved  in  these  results  ? 
When  does  rotation  ensue  ? 


116  THE   PENDULUM. 

in  the  same  vertical  line,  they  counteract  each  other ;  but 
in  any  other  position  a  movement  of  rotation  must  ensue. 
The  solid,  therefore,  turns  over,  and  finally  comes  into 
such  a  position  as  satisfies  the  conditions  of  equilibrium. 
On  these  principles  a  cube  will  float  on  any  one  of  its 
faces,  and  a  sphere  in  any  position  whatever ;  but  if  the 
sphere  be  not  of  uniform  density,  one  part  of  it  being 
heavier  than  the  rest,  motion  takes  place  until  the  heaviest 
part  is  lowest.  A  long  cylinder  floating  on  its  end  is 
unstable,  but  when  it  floats  lengthwise,  stable.  It  is 
obvious  these  principles  are  of  great  importance  in  ship- 
building, and  the  loading  and  ballasting  of  ships. 


LECTURE  XXV. 

THE    PENDULUM. — Simple   and  Physical   Pendulums. — 
Nature  of  Oscillatory  Motion. — Center  of  Oscillation., 
— Laws    of  Pendulums. —  Cycloidal    Vibrations. —  The 
Seconds1   Pendulum. — Measures   of  Time,   Space,   and 
Gravity. — Compensation  Pendulums. 

A  SOLID  body  suspended  upon  a  point  with  its  center 
of  gravity  below,  so  that  it  can  oscillate  under  the  influ- 
ence of  gravity,  is  called  a  pendulum. 

A  simple  pendulum  is  imagined  to  consist  of  an  im- 
ponderable line,  having  freedom  of  motion  at  one  end, 
and  at  the  other  a  point  possessing  weight. 

A  physical  pendulum  consists  of  a  heavy  metallic  ball 
suspended  by  a  thread  or  slender  wire. 

The  position  of  rest  of  a  pendulum  is  when  its  center 
of  gravity  is  perpendicularly  beneath  its  point  of  suspen- 
sion, its  length,  therefore,  is  in  the  line  of  direction.  If 
it  be  removed  from  this  position,  it  returns  to  it  again 
after  making  several  oscillations  backward  and  forward. 
Its  descending  motions  are  due  to  the  gravitating  action 
of  the  earth,  its  ascending  due  to  its  own  inertia.  A 
pendulum  once  in  motion  would  vibrate  continually  were 
it  not  for  friction  on  its  point  of  suspension,  the  rigidity 

Give  examples  of  the  flotation  of  different  bodies.  What  is  a  pendu- 
lum ?  What  is  the  difference  between  a  simple  and  a  physical  pendulum  7 
What  is  the  position  of  rest  ?  What  is  the  effect  of  removal  from  that  po- 
sition ?  Why  does  the  instrument  eventually  come  to  rest  ? 


THE    PENDULUM. 


117 


of  the  thread,  if  it  be  supported  by  one,  and  the  resistance 
of  atmospheric  air. 

The  length  of  a  pen-  Fig.  131. 

dulum  is  the  distance 
that  intervenes  between 
its  point  of  suspension 
and  its  center  of  oscil- 
lation. Its  oscillation  is 
the  extreme  distance 
through  which  it  passes 
from  the  right  hand  to 
the  left,  or  from  the  left 
to  the  right.  In  Fig. 
131,  a  is  the  point  of 
suspension,  b  the  center 
of  oscillation ;  a  b  the 
length  of  the  pendulum; 
c  b  d  or  d  b  c  the  oscil- 
lation ;  the  angle  a  or 
Q  is  the  angle  of  elongation ;  and  the  time  is  the  period 
that  elapses  in  making  one  complete  oscillation.  Oscilla- 
tions are  said  to  be  isochronous  when  they  are  performed 
in  equal  times. 

Let  a  b  c,  Fig.  132,  be  a  pendulous  body,  supported  on 
the  point  «,  and  performing  its  oscillations       fig- 132- 
upon  that  point.    If  we  consider  the  motions 
of  two  points,  such  as  b  and  c,  it  will  appear 
that  under  the  influence  of  gravity  the  point 

b,  which  is  nearer  to  the  point  of  suspension, 
would  perform  its  oscillations  more  quickly 
than  the  point  c.    But  inasmuch  as  in  the  pen- 
dulous body  both  are  supposed  to  be  inflex- 
ibly connected  together,  by  reason  of  the  so- 
lidity of  the  mass,  both  are  compelled  to  per- 
form their  oscillations  in  the  same  time.  The 

point  b  will,  therefore,  tend  to  accelerate  the  motions  of 

c,  and  c  will  tend  to  retard  the  motions  of  b.     It  follows, 
therefore,  that  in  every  pendulum  there  is  a  point  the 
velocity  of  which,  multiplied  by  the  mass  of  the  pendu- 
lum, is  equal  to  the  quantity  of  motion  in  the  pendulum. 


What  is  the  length  of  a  pendulum,  the  point  of  suspension,  the  oscilla- 
tion, the  angle  of  elongation,  and  the  time  ? 


118  CENTER    OF    OSCILLATION. 

To  this  point  the  name  of  center  of  oscillation  is  given. 
In  a  linear  pendulum — that  is,  a  rod  of  inappreciable 
thickness — the  center  of  oscillation  is  two  thirds  the  length 
from  the  point  of  suspension.  In  a  right-angled  conical 
mass  the  center  of  oscillation  is  at  the  center  of  the  base. 

The  center  of  oscillation  possesses  the  remarkable 
property  that  it  is  convertible  with  the  centre  of  suspen- 
sion— that  is  to  say,  if  a  pendulum  vibrates  in  a  given 
time,  when  supported  on  its  ordinary  centre  of  suspen- 
sion, it  will  vibrate  in  the  same  time  exactly  if  it  be  sus- 
pended on  its  center  of  oscillation.  Advantage  has  been 
taken  of  this  property  to  determine  the  lengths  of  pendu- 
lums, with  great  precision,  and  thereby  the  intensity  of 
gravity  and  the  figure  of  the  earth.  In  these  cases  a  sim- 
ple bar  of  metal,  of  proper  length,  with  knife-edges  equi- 
distant from  its  ends,  has  been  used  and  adjustment  made 
until  the  bar  vibrated  equally  when  supported  on  either 
knife  edge.  The  distance  between  the  knife-edges  is  the 
length  of  the  pendulum. 

Pendulums  of  equal  lengths  vibrate  in  the  same  place 
in  equal  times,  provided  their  angles  of  elongation  do  not 
exceed  two  or  three  degrees. 

Pendulums  of  unequal  lengths  vibrate  in  unequal  times 
— the  shorter  more  quickly  than  the  longer — the  times  be- 
ing to  one  another  as  the  square  roots  of  the  lengths  of 
the  pendulums. 

fig- 133.  If  we  take  a  circle,  B,  Fig. 

— 3)133,  and,  causing  it   to  roll 
along  a  plane,  B  D,  mark  out 
the  path  which  is  described 
by  a  point,  P,  in  its  circum- 
ference, the  line  so  marked  is  designated  a  cycloid. 

When  a  pendulum  vibrates  in  a  cycloid,  it  will  describe 
all  arcs  thereof  in  equal  times ;  and  the  time  of  each  os- 
cillation is  to  the  time  in  which  a  heavy  body  would  fall 
through  half  the  length  of  the  pendulum  as  the  circum- 
ference of  a  circle  is  to  its  diameter. 

The  difference,  therefore,  between  oscillation  in  cy- 

Describe  the  nature  of  the  center  of  oscillation.  What  is  its  position 
in  a  linear  pendulum  and  in  a  right-angled  conical  mass?  What  property 
does  the  center  of  oscillation  possess?  What  are  the  laws  of  the  mo- 
tion of  pendulums  ?  What  is  a  cycloid  ?  What  property  does  a  pendu- 
lum vibrating  in  a  cycloid  possess  ? 


LENGTH  OP  THE  PENDULUM.          119 

cloidal  and  circular  arcs  is,  that  in  the  former  all  oscilla- 
tions are  isochronous,  but  in  the  latter  they  are  not ;  for 
the  larger  the  circular  arc  the  longer  the  lime  of  oscilla- 
tion. And  as  circular  movement  is  the  only  one  which 
can  be  conveniently  resorted  to  in  practice,  it  is  necessa- 
ry to  reduce  circular  to  cy cloidal  oscillations  by  calcula- 
tion. 

When  the  length  of  the  pendulum  is  such  that  its  time 
of  oscillation  is  equal  to  one  second,  it  is  called  a  seconds' 
pendulum.  This  length  differs  at  different  places.  Un- 
der the  equator  it  is  shorter  than  at  the  poles  ;  and  this 
evidently  arises  from  the  circumstance  that  the  intensity 
of  gravity,  as  has  been  already  explained,  is  different  at 
those  points ;  for  the  figure  of  the  earth  not  being  a  per- 
fect sphere  but  an  oblate  spheroid,  its  polar  axis  being 
shorter  than  its  equatorial,  a  body  at  the  poles  is  more 
powerfully  attracted  than  one  at  the  equator,  it  being 
nearer  the  center  of  the  earth  ;  and  as  the  motion  of  the 
pendulum  arises  from  gravity,  in  order  to  make  it  oscil- 
late in  equal  times,  it  is  necessary  to  have  it  shorter  at  the 
equator  than  at  the  pole.  The  length  of  the  seconds'  pen- 
dulum in  Londoa  is  39.13929  inches,  at  a  temperature  of 
60°  Fahrenheit. 

For  many  of  the  purposes  of  physical  science  the  pen- 
dulum is  an  important  instrument.  It  affords  us  the  best 
measure  of  time,  and  is,  therefore,  used  in  all  stationary 
timepieces  or  clocks.  A  clock  is  a  mechanical  apparatus 
for  the  purpose  of  registering  the  numbers  of  oscillations 
which  a  pendulum  makes,  and  at  the  same  time  of  com- 
municating to  the  pendulum  the  amount  of  motion  it  is 
continually  losing  by  friction  on  its  points  of  support  and 
by  resistance  of  the  air.  The  oscillations  are  performed 
in  small  circular  arcs,  so  that  the  times  are  equal. 

Whatever  affects  the  length  of  the  pendulum  changes 
the  time  of  its  motion.  It  is  for  this  reason  that  clocks 
go  slower  in  summer  and  faster  in  winter — the  changes 
of  temperature  altering  the  length  of  the  pendulum.  To 
compensate  this,  various  contrivances  have  been  resorted 
to  with  a  view  of  securing  the  invariability  of  the  instru- 

What  difference  is  there  between  oscillation  in  cycloidal  and  circular 
arcs  ?  What  is  a  seconds'  pendulum  ?  Is  there  difference  in  its  length  at 
different  places  ?  From  what  does  this  arise  ?  What  is  the  pendulum- 
clock  ?  Why  do  variations  of  temperature  change  the  rate  of  a  clock  ? 


120 


THE    MERCURIAL    PENDULUM. 


ment.     The  nature  of  these  is  very  well  illustrated  by  the 
mercurial  pendulum. 

Fig.  134.  Let  A  B  be  the  pendulum-rod  :  at  B  it  is 

formed  into  a  kind  of  rectangle,  F  G  D  E, 
within  which  is  placed  a  glass  jar,  G  H,  con- 
taining mercury,  and  serving  as  the  bulb  of 
the  pendulum.  When  the  weather  becomes 
warm,  the  steel-rod  and  rectangle  elongate, 
and  therefore  depress  the  center  of  oscilla- 
tion. But  simultaneously  the  mercury  ex- 
pands, and  this  motion  takes  place  necessa- 
rily in  the  upward  direction.  If  the  quan- 
tity of  mercury  is  properly  adjusted  the  cen- 
ter of  oscillation  is  carried  as  far  upward  by 
the  mercurial  expansion  as  downward  by 
that  of  the  steel.  Its  actual  position  remains, 
therefore,  the  same;  and  as  the  length  of  the 
pendulum  is  the  distance  between  the  point 
E  of  suspension  and  center  of  oscillation,  that 
length  remains  unchanged.  The  gridiron 
pendulum  acts  on  similar  principles. 

The  pendulum  is  also  i^sed  to  determine 
the  force  of  gravity.  The  nature  of  this  ap- 
plication has  already  been  pointed  out  in 
what  has  been  said  respecting  oscillations 
at  the  equator  and  the  poles.  The  force  of 
gravity  at  any  place,  or  the  height  through 
which  a  body  will  fall  in  one  second  is  de- 
termined by  multiplying  the  lengths  of  a 
seconds'  pendulum  for  that  place  by  the  number  4.9348. 
The  length  of  the  seconds'  pendulum  being  always  in- 
variable at  the  same  place — for  gravity  is  always  invaria- 
ble— may  be  used  as  a  standard  of  measure.  Thus,  the 
English  inch  is  of  such  a  length  that  39.13939  inches  are 
equal  to  the  length  of  a  pendulum  vibrating  seconds. 
From  these  measures  of  length,  measures  of  capacity 
might  be  derived  by  taking  their  cubes,  and  measures  of 
surface  by  taking  their  squares. 

What  contrivances  have  been  resorted  to  to  avoid  this  difficulty  (  De- 
scribe the  mercurial  pendulum.  On  what  principle  is  the  pendulum  used 
to  determine  the  force  of  gravity  ?  Under  what  circumstances  may  the 
pendulum  be  used  as  a  standard  of  measure  ? 


PERCUSSION. 


LECTURE  XXVI. 

OF  PERCUSSION. — Of  Impact,  Central,  Excentric,  Direct, 
Oblique. — Inelastic  and  Elastic  Bodies. — Laws  of  Col- 
lision of  Inelastic  Bodies. — Changes  of  Figure  of  Elastic 
Bodies. — Phenomena  of  their  Collision. — Of  Reflected 
Motions. 

IMPACT  or  percussion  may  take  place  in  several  differ- 
ent ways — as  central,  excentric,  direct,  oblique. 

Central  impact  takes  place  when  the  bodies  in  collision 
have  their  centers  of  gravity  moving  in  the  same  right 
line. 

Excentric  impact  is  when  the  directions  of  the  motion 
of  the  centers  of  gravity  of  the  bodies  in  collision  make  an 
angle  with  one  another. 

Direct  impact  is  when  the  direction  of  the  moving 
body  is  perpendicular  to  the  surface  on  which  it  impinges. 

Oblique  impact  is  when  the  direction  of  the  moving 
body  makes  some  angle  other  than  a  right  one  with  the 
surface  on  which  it  impinges. 

The  phenomena  of  percussion  depend  greatly  on  the 
physical  character  of  the  impinging  bodies.  The  bodies 
may  either  be  inelastic  or  elastic.  Masses  of  clay  or  putty 
are  illustrations  of  the  former  case,  balls  of  ivory  or  steel 
of  the  latter. 

It  has  already  been  shown,  Lecture  XVII,  that  if  two 
inelastic  bodies  move  in  the  same  direction  their  joint  mo- 
mentum, after  impact,  is  equal  to  the  sum  of  their  sepa- 
rate momenta ;  and  that,  if  they  move  in  opposite  direc- 
tions, it  is  equal  to  the  difference.  Their  velocity,  after 
impact,  is  found  by  dividing  their  common  momentum  by 
the  sum  of  their  masses. 

When  a  hard  body  impinges  on  an  immovable  mass, 
the  particles  of  which  can,  however,  recede,  so  as  to  ad- 

What  is  central  impact  ?  What  are  excentric,  direct,  and  oblique  ?  On 
what  physical  character  do  the  phenomena  of  percussion,  to  a  great  ex- 
tent depend  ?  Give  examples  of  inelastic  and  elastic  solids.  What  are 
the  laws  of  motion  of  inelastic  bodies  ? 

F 


122 


ELASTIC    IMPACT. 


mit  the  impinging  body,  the  depths  to  which  it  will  pene- 
trate are  as  the  squares  of  its  velocity  multiplied  by  its 
mass. 

When  elastic  bodies  impinge  on  each  other,  there  is, 
Fig.  135.  during  the  time  of  their  encoun- 

ter, a  change  of  figure.  Thus, 
if  we  take  the  instrument,  Fig. 
135,  and,  having  painted  one  of 
its  ivory  balls,  a,  let  the  other 
ball,  b,  touch  it  gently,  the  latter 
will  receive  on  its  surface  a  sin- 
gle point  of  paint.  But  if  we, 
raise  this  ball,  and  let  it  fall  from 
a  considerable  distance  upon  the 
other,  it  will  receive  a  circular  mark  of  paint,  showing 
that,  during  the  percussion,  the  balls  lost  their  spherical 
figure,  and,  instead  of  touching  by  a  single  point,  they 
touched  by  a  surface  of  considerable  extent.  Their  in- 
stantaneous recovery  of  the  spherical  form,  like  the  fa- 
cility with  which  that  form  was  lost,  is  due  to  their  elas- 
ticity. 

Whatever  tends  to  impair  the  elasticity  of  such  balls 
tends,  therefore,  to  change  the  phenomena  of  impact. 
Thus,  if  we  make  a  cavity  in  one  of  them,  and  fill  it  par- 
tially with  lead,  the  balls,  after  percussion,  will  not  re- 
cede from  one  another  as  far  as  before. 

The  manner  in  which  elasticity  acts  in  these  cases  may 
be  understood  by  considering  the  action  of  a  spiral  spring 
between  the  two  balls,  the  length  of  it  coinciding  with 
the  direction  of  their  motion.  When  the  balls  fall  upon 
its  extremities,  they  give  rise  to  compression,  and  the 
spring  continually  resists  them  at  each  successive  instant. 
Their  force,  which  was  greatest  at  the  moment  of  impact, 
is  gradually  overcome  by  the  resistance  of  the  spring, 
and  finally  vanishes.  As  soon  as  their  velocity  ceases, 
the  spring  can  undergo  no  further  compression,  and  is 
now  able  to  begin  to  restore  itself  with  a  continually  in- 
creasing force.  Finally,  it  communicates  to  the  balls 
the  same  velocity  with  which  they  originally  impinged 
upon  it. 

What  is  the  nature  of  the  change  of  figure  which  elastic  bodies  exhibit 
when  they  encounter  '>.  How  may  this  be  proved  ?  How  may  it  be  illus- 
trated by  the  action  of  a  spring  ? 


ELASTIC  IMPACT. 


123 


When,  therefore,  a  pair  of  elastic  spherical  balls  are 
made  to  impinge  on  each  other,  there  Fig.  136. 

is  a  compression  of  their  particles  in 
the  direction  in  which  the  motion  is 
taking  place,  so  that  the  diameters,  cj 
a  b,  a  c,  Fig.  136,  are  less  than  be- 
fore. A  spheroidal  form  is,  there- 
fore, the  necessary  result.  But  just 
as  with  the  imaginary  spring  in  the  foregoing  case  so  with 
the  compressed  particles  in  this.  As  soon  as  the  motion 
of  the  bodies  becomes  0,  the  elastic  force  of  the  compress- 
ed particles  gives  rise  to  movement  in  the  opposite  di- 
rection. 

When  two  perfectly  elastic  bodies  come  in  collision,  the 
force  of  elasticity  is  equal  to  the  force  of  compression,  and 
the  force  of  compression  is  equal  to  the  force  of  the  shock. 

When  two  elastic  bodies  have  struck  each  other,  their 
recession  will  be  with  the  same  relative  velocity  with 
which  they  fell  upon  each  other. 

When  two  equal  elastic  bodies  move  toward  each 
other  with  equal  velocities,  after  percussion  they  recede 
from  each  other  with  the  same  velocity. 

When  of  two  equal  elastic  bodies  fig- 137. 

one  is  in  motion  and  the  other  at 
rest,  the  former,  after  collision, 
will  communicate  to  the  other 
all  its  velocity,  and  remain  at 
rest  itself.  This  phenomenon, 
and  indeed  much  that  is  here 
said  in  relation  to  the  impact  of 
bodies,  is  well  shown  by  an  ap- 
paratus such  as  Fig.  137,  in 
which  let  the  ball,  a,  be  at  rest,  and  let  b  fall  on  it  from 
any  height,  after  collision,  a  takes  the  whole  velocity  of 
b,  and  b  itself  remains  at  rest. 

When  of  two  equal  bodies,  moving  in  the  same  direc- 
tion, one  overtakes  the  other,  they  exchange  velocities 
and  go  on  as  before. 

When  two  equal  bodies,  moving  with  different  veloci- 
ties, encounter  each  other,  they  exchange,  and  recede  from 
one  another  in  contrary  directions. 

What  are  the  laws  of  motion  of  perfectly  elastic  bodies  ?  How  may 
these  be  proved  experimentally  ? 


124  ELASTIC    BODIES. 

If,  in  the  instrument  Fig.  137,  instead  of  having  only 
two  ivory  balls,  we  had  a  large  number  suspended,  so  as 
to  touch  one  another,  it  would  be  found,  on  letting  the 
ball  at  one  extremity  impinge  on  the  others,  that  all  the 
intermediate  ones  would  remain  motionless,  and  the  one 
at  the  farther  extremity  would  rebound.  The  motion, 
therefore,  is  transmitted  through  the  entire  series  of  baljs  ; 
and  it  is  the  mutual  reaction  of  the  intermediate  ones  which 
keeps  them  at  rest,  the  distant  one  rebounding  because 
there  is  nothing  against  which  it  can  react. 

Fig.  138.  When  an  elastic  ball  strikes  upon 

c    an  immovable  elastic  plane  it  will 
recoil  with  the  same  velocity  with 
which   it  advanced.     When    the 
impact  is  perpendicular,  the  path  of 
retrocession  is  the  same  as  that  of 
advance.    Thus,  if  a  b,  Fig.  138, 
be  the  path  of  the  advance,  per- 
pendicular to  c  d,  the  elastic  plane, 
the  recoil  or  retrocession  will  be 
in  the  same  path,  but  in  the  op- 
posite direction,  b  a. 
When  the  path  of  the  striking  body  is  not  perpendicu- 
lar, but  at  some  other  angle  to  the  elastic  plane  the  recoil 
Fig.  139.       will  be  under  the  same  angle,  but  on  the  op- 


\d 
\ 

\ 


ja,  posite  side  of  the  perpendicular.  Thus/if 
a  c,  Fig.  139,  be  the  path  of  the  striking 
body,  c,  the  elastic  plane,  the  path  after  con- 
-,  /  tact  will  be  c,  d,  such  that  the  points  a  c  d, 
are  in  the  same  plane,  and  the  angle  a  c  b  is 
equal  to  the  angle  bed.  To  the  former  of 
these  the  name  "  angle  of  incidence"  is  given,  to  the  lat- 
ter "  angle  of  reflexion." 

The  angle  of  incidence  is  the  angle  included  between 
the  path  of  the  impinging  body  and  a  perpendicular,  b  c, 
drawn  to  the  surface  of  impact  at  the  point  of  impact 
And  the  angle  of  reflexion  is  the  angle  included  between 
the  path  of  the  retroceding  body  and  the  same  perpen- 
dicular. 

The  principles  given  in   this  Lecture  are   applied  in 

What  are  the  laws  of  motion  of  an  elastic  ball  striking  upon  an  immova- 
ble elastic  plane  ?  What  is  meant  by  the  angle  of  incidence  ?  What  is 
thb  angle  of  reflexion  ? 


PERCUSSION.  125 

many  cases  of  practice.  Thus,  in  the  pile  engine,  which 
consists  of  a  heavy  block,  raised  slowly  by  machinery  be- 
tween two  uprights,  and  then  allowed  to  fall  suddenly  on 
the  head  of  the  pile  to  be  driven  into  the  ground.  If  the 
block  thus  used  as  a  hammer  is  too  small,  it  fails  to  move 
the  pile ;  and  if  its  velocity  is  too  great  it  splits  the  head 
of  the  pile.  A  large  mass,  falling  from  a  small  height,  is 
therefore  used.  Thus  it  may  be  readily  shown,  that  if 
the  hammer  weighs  1000  pounds,  and  it  falls  through  a 
height  of  only  four  feet,  the  force  with  which  it  strikes 
the  pile  is  equal  to  120,000  pounds. 

When  gold  is  beaten  into  thin  leaves  the  workmen  can- 
not employ  light  hammers  and  use  them  quickly,  for  they 
would  divide  or  fissure  the  gold  :  they  use,  therefore, 
heavier  hammers,  and  move  them  more  slowly. 

Give  some  illustrations  of  the  phenomena  of  impact. 


126  MACHINES. 


THE  ELEMENTS  OF  MACHINERY. 


LECTURE  XXVII 

THE  MECHANICAL  POWERS. — Definition  of  MacJiines. — 
Number  of  Mechanical  Powers. — Power. —  Weight. — 
Principle  of  Virtual  Velocities. 

THE  LEVER — Definition  of. —  Three  Kinds  of  Lever. — 
Conditions  of  Equilibrium. —  Uses  of  Levers. —  The  Bal- 
ance.—  Weighing  Machines. 

BY  MACHINES  are  meant  certain  contrivances  employed 
for  the  purpose  of  changing  the  direction  of  moving  pow- 
ers, or  of  enabling  them  to  produce  any  required  velocity, 
or  to  overcome  any  required  force. 

It  is  to  be  understood  that  the  force  of  any  moving 
power  can  never  be  increased  by  the  agency  of  any  ma- 
chine the  duty  of  which  is  to  transmit  the  effect  of  that 
power  unimpaired  to  the  working  point.  Machinery 
cannot  create  power — it  transmits  it.  Theoretically,  this 
transmission  is  supposed  to  take  place  without  loss,  but 
practically  there  is  always  a  certain  degree  of  diminution 
arising  both  from  imperfections  of  construction  and  the 
agency  of  such  impediments  to  motion  as  friction,  rigidi- 
ty, &c.,  the  consideration  of  which  we  shall  resume  in  its 
proper  place. 

In  what  follows,  it  will,  therefore,  be  understood  that 
we  speak  of  the  action  of  machines  theoretically,  and 
apart  from  the  intervention  of  these  disturbing  causes. 

All  machines,  no  matter  how  complex  soever  their  con- 
struction may  be,  can  be  reduced  to  one  or  more  of  six 

What  is  meant  by  a  machine  ?  Can  machines  create  power?  What 
is  the  difference  between  the  theoretical  and  practical  action  of  machines? 
How  many  simple  machines  are  there  ? 


PRINCIPLE   OF    VIRTUAL  VELOCITIES.  127 

simpler  elements,  which  pass  under  the  name  of  the  "  me- 
chanical powers."     They  are, 

The  Lever, 
Pulley, 

Wheel  and  axle, 
Inclined  plane, 
Wedge, 
Screw. 

These  mechanical  powers,  or  simple  machines,  may, 
indeed,  be  further  reduced  to  three  : 

The  Lever, 
Pulley, 
Inclined  plane. 

In  any  machine  the  force  or  original  prime-mover  passes 
under  the  name  of  THE  POWER. 

The  resistance  to  be  overcome,  or  that  upon  which  the 
power  is  brought  to  bear  through  the  intervention  of  the 
machine,  goes  under  the  name  of  THE  WEIGHT. 

The  general  law  which  determines  the  equilibrium  of 
all  machines,  whether  simple  or  compound,  is  as  follows : 
"  The  power  multiplied  by  the  space  through  which  it  moves 
in  a  vertical  direction  is  equal  to  the  weight  multiplied  by 
the  space  through  which  it  moves  in  a  vertical  direction" 
The  principle  involved  in  this  law  passes  under  the  name 
of  "  the  principle  of  virtual  velocities." 

The  foregoing  principle  expounding  the  conditions  un- 
der which  the  power  and  weight  are  in  equilibrium,  and 
the  machine,  therefore,  in  a  state  of  rest,  it  follows,  there- 
fore, that  "  if  the  product  arising  from  the  power  multi- 
plied by  the  space  through  which  it  moves  in  a  vertical  di- 
rection, be  greater  than  the  product  arising  from  the  weight 
multiplied  by  the  space  through  which  it  moves  in  a  verti- 
cal direction,  the  power  will  overcome  the  resistance  of  the 
weight,  and  motion  of  the  machine  will  ensue" 

THE    LEVER. 

The  lever  is  the  first  of  the  elementary  machines.  In 
theory,  it  is  an  inflexible  and  imponderable  line  supported 
on  one  point  on  which  it  can  turn.  In  practice,  it  con- 
To  what  may  these  be  further  reduced  ?  What  is  the  power?  What 
is  the  weight  ?  Describe  the  general  law  of  equilibrium  of  all  machines. 
What  name  is  given  to  the  principle  contained  in  this  law  ?  Under  what 
condition  does  motion  ensue  ?  What  is  a  lever  ( 


128  VTHE    LEVER. 

sists   of  a  solid  unyielding  rod  working  upon  a  point 
called  a  fulcrum. 

Three  varieties  of  lever  are  commonly  enumerated.     In 

HO  tlie  ^rst'  ttie  fulcrum»  F,  is  between  the 

tg'    i*'  power,  P,  and  the  weight,  W,  as  in  Fig. 

pi  TfQ       i40t     In  the  second,  the  weight  is  be- 

Fig.  MI.  tween  the  power  and  the  fulcrum,  Fig. 

fjH  141.     In  the  third,  the  power  is  between 

the  weight   and  the  fulcrum,  Fig.  142. 


Fig.  142.  There  are   also   other  species  of  lever, 

pa  such  as  the  bent  lever,  the  curvilinear 

lever.     The  mode  of  action  and  theory 


of  all  are  the  same. 

By  the  principle  of  virtual  velocities,  it  appears  that 
"  any  lever  is  in  equilibria  when  the  power  and  the  weight  are 
to  each  other  inversely  as  their  distances  from.  the  fulcrum'' 

As  illustrative  instances  of  this  —  if  in  a  lever  of  the 
first  kind,  in  equilibria,  the  power  and  the  weight  are  equal, 
they  must  be  at  equal  distances  from  the  fulcrum.  If  the 
power  is  only  half  the  weight,  it  must  be  at  double  the 
distance  from  the  fulcrum,  if  one  third  the  weight,  triple 
the  distance,  &c. 

When,  therefore,  it  is  proposed  by  the  intervention  of 
a  lever  to  cause  a  given  power  to  overcome  a  given 
weight,  it  is  necessary  that  the  power  multiplied  by  its 
distance  from  the  fulcrum  should  give  a  greater  product 
than  the  weight  multiplied  by  its  distance  from  the  ful- 
Fiff.  143.  crum.  Thus,  in  Fig.  141,  let 

1  P  be  a  power  of  six  pounds, 


w6 

7 


p  operating  on  a  lever  of  the 
first  kind,  at  a  distance,  p  c, 
from  the  fulcrum,  c,  of  seven 
inches  ;  let  W  be  the  weight 
to  be  overcome,  and  let  it  be 
seven  pounds,  with  a  distance, 
W  c,  of  six  inches  from  the 

fulcrum.  Now  the  power  multiplied  into  its  distance 
is  equal  to  forty-two,  and  the  weight  multiplied  into  its 
distance  is  also  equal  to  forty-two  ;  the  lever  is,  therefore, 
under  the  law  just  stated  in  equilibrio.  But  if  we  in- 
crease the  distance  of  P  from  c,  or  increase  P  itself,  or  do 

How  many  varieties  of  it  are  there  ?  What  is  the  law  of  equilibrium  of 
the  lever  ?  Give  an  illustration  of  it  ? 


THE    LEVER. 


129 


both,  then  the  product  of  P  into  its  distance  from  the 
fulcrum  will  increase,  the  lever  will  move,  and  the  resist- 
ance of  the  weight  be  overcome. 

Levers  are  used  in  practice  for  many  different  purposes. 
By  their  agency  a  small  power  may  hold  in  equilibrio,  or 
move  a  great  weight;  thus,  the  power  of  one  man  applied 
at  the  end  of  a  crowbar  will  overturn  a  heavy  mass,  the 
man  acting  at  a  distance  of  several  feet,  and  the  mass  at 
only  a  few  inches  from  the  fulcrum.  Of  levers  of  the 
first  kind,  crowbars  and  scissors  are  familiar  examples. 
Of  those  of  the  second  kind,  oars  and  nutcrackers ;  of 
those  of  the  third,  tongs  and  sheepshears. 

For  many  of  the  purposes  of  science  levers  are  used  to 
magnify  small  motions.  The  power  causing  the  motion 
is  applied  by  a  short  arm  near  to  the  fulcrum  of  the  lever, 

Fig.  144. 


Mention  some  of  the  applications  of  the  lever.    Give  familiar  instances 
of  each  of  the  three  kinds  of  lever. 


130  THE    BALANCE. 

and  the  other  arm.  which  may  be  ten,  twenty,  or  more 
times  longer,  moves  over  a  graduated  scale.  The  py- 
rometer is  an  example  of  this  application. 

The  most  accurate  means  for  determining  the  weight 
of  bodies  is  by  the  lever.  When  arranged  for  this  pur- 
pose, it  passes  under  the  name  of  "  The  Balance."  It  is 
a  lever  of  the  first  kind  with  equal  arms.  Various  forms 
are  given  to  it,  and  various  contrivances  annexed  for  the 
purpose  of  insuring  its  lightness,  its  inflexibility,  and  the 
absolute  equality  of  the  lengths  of  its  arms.  Fig.  144, 
represents  one  of  the  best  kinds :  a  a  is  the  beam ;  c  is 
the  fulcrum,  or  center  of  motion ;  d  d  are  the  scale-pans 
in  which  the  weights  and  objects  to  be  weighed  are 
applied ;  their  points  of  suspension  are  at  a  a.  With  a 
view  of  reducing  friction,  the  axis  of  motion,  c,  and  both 
the  points  of  suspension  are  knife-edges  of  hard  steel 
working  on  planes  of  agate ;  and,  to  preserve  them  unin- 
jured, the  beam  and  the  scale-pans  are  supported  upon 
props,  except  at  the  time  a  substance  is  to  be  weighed. 
Then,  by  moving  the  handle,  f,  the  axis  of  motion  is  de- 
posited slowly  on  its  agate  plane,  and  the  scale-pans  on 
their  points  of  suspension,  and  the  beam  thrown  into  action. 

In  balances  it  is  essential  that  the  center  of  gravity 
should  have  a  particular  position.  The  cause  of  this 
will  be  appreciated  from  what  has  been  said  in  Lecture 
XXIV.  Thus,  if  the  center  of  gravity  coincided  with 
the  center  of  motion,  the  balance  beam  would  not  vibrate, 
but  would  stand  in  a  position  of  indifferent  equilibrium, 
whatever  angular  position  might  be  given  to  its  arms. 

If  the  centre  of  gravity  was  above  the  axis  of  motion, 
the  balance  would  be  in  a  condition  of  unstable  equilib- 
rium, and  would  overset  by  the  slightest  increase  of 
weight  on  either  side,  the  center  of  gravity  coming  down 
to  the  lowest  point.  But  when  it  is  beneath  the  axis  of 
motion,  the  balance  vibrates  like  a  pendulum,  and  neither 
sets  nor  oversets.  It  is  essential,  therefore,  that  in  all 
these  instruments  the  center  of  gravity  should  be  below 
the  center  of  motion.  And  it  might  be  shown  that  the 

Give  an  instance  of  the  application  of  the  lever  to  magnifying  small 
motions.  What  is  a  balance  ?  What  takes  place  if  the  center  of  gravity 
coincides  with  the  center  of  motion  ?  What  is  the  effect  when  it  is  above 
the  axis  of  motion  ?  What  when  it  is  beneath  ?  With  what  does  the 
sensibility  of  the  balance  increase  ? 


WEIGHING    MACHINES. 


131 


sensibility  of  the  balance,  or,  in  other  words,  the  small- 
ness  of  the  weight  it  will  detect,  becomes  greater  as 
these  two  centers  approach  each  other. 

The  different  kinds  of  weighing-machines  are  either 
modified  levers  or  combinations  of  levers.  Examples  oc- 
cur in  the  machine  for  weighing  Fig.  145. 
loaded  carts,  in  the  steelyard, 
which  is  a  lever  of  unequal  arms, 
and  in  the  bent  lever  balance. 
The  latter  is  represented  in  Fig. 
145.  It  consists  of  a  bent  lever, 
ABC,  the  end  of  which,  C,  is 
loaded  with  a  fixed  weight.  This 
lever  works  on  a  fulcrum,  B, 
supported  on  a  pillar,  H  J.  From 
the  arm,  A,  is  suspended  a  scale- 
pan,  E,  and  to  the  pillar  there  is 
affixed  a  divided  scale,  F  G,  over 
which  the  lever  moves.  Through 
B  draw  the  horizontal  line,  G  K,  and  let  fall  from  it  the 
perpendiculars,  A  K,  D  C.  Then,  if  B  K  and  B  D  are 
inversely  proportional  to  the  weight  in  the  scale,  E,  and 
the  fixed  weight,  C,  the  balance  will  be  in  equilibrio  ; 
but  if  they  are  not,  then  the  lever  moves,  C  going  farther 
from  the  fulcrum,  and  stopping  when  equilibrium  is  at- 
tained. The  scale,  F  G,  is  graduated  by  previously  put- 
ting known  weights  in  E. 


LECTURE  XXVIII. 

THE  PULLEY. — Description  of  the  Pulley. — Laws  of  the 
Lever  apply  to  it. —  Use  of  the  Fixed  Pulley. —  The 
Movable  Pulley. —  Runners. —  Systems  of  Pulleys. — 
White's  Pulley. 

THE  WHEEL  AND  AXLE. — Law  of  Equilibrium. — Advan- 
tages over  the  Lever. —  Windlass. — Capstan.— Wheel- 
work. — Different  kinds  of  TootJied-WJieels. 

THE  pulley  is  a  wheel,  round  the  rim  of  which  a  groove 
is  cut,  in  which  a  cord  can  work,  and  the  center  of  which 


Describe  the  bent  lever  balance  and  the  steelyard, 
sheave,  and  its  block  ? 


What  is  a  pulley,  its 


132  THE    FIXED    PULLEY. 

moves  on  pivots  in  a  block.  The  wheel  sometimes  passes 
under  the  name  of  a  sheave. 

By  a  fixed  pulley  we  mean  one  which  merely  revolves 
on  its  axis,  but  does  not  change  its  place.  The  power 
is  applied  to  one  end  of  the  cord  and  the  weight  to  the 
other. 

Fig.  146.  The  action  of  the  pulley  may  be 

readily  understood  from  that  of  the 
lever.  Let  c,  Fig.  146,  be  the  axis 
of  the  pulley,  b  the  point  to  which 
the  weight  is  attached,  a  the  point 
of  application  of  the  power  ;  draw 
the  lines,  c  b,  c  a — they  represent 
the  arms  of  a  lever — and  the  law  of 
the  equilibrium  of  a  lever,  therefore, 
applies  in  this  case  also  ;  and,  as 
these  arms  are  necessarily  equal  to 
each  other,  the  pulley  will  be  in  equilibrio  when  the 
weight  and  power  are  equal. 

If  the  direction  in  which  the  power  is  applied,  instead 
of  being  P  a,  is  P'  a,  the  same  reasoning  still  holds  good. 
For,  on  drawing  C  a,  as  before,  it  is  obvious  that  b  c  a 
represents  a  bent  lever  of  equal  arms.  The  condition  of 
equilibrium  is,  therefore,  the  same. 

The  fixed  pulley  does  not  increase  the  power,  but  it 
renders  it  more  available,  by  permitting  us  to  apply  it  in 
any  desired  direction. 

To  prove  the  properties  of  the  pulley  experimentally, 
hang  to  the  ends  of  its  oord  equal  weights ;  they  will  re- 
main in  equilibrio.  Or,  if  the  power  be  increased,  so  as 
to  make  the  weight  ascend,  the  vertical  distances  passed 
over  are  equal. 

The  movable  pulley  is  represented  at  Fig.  147.  Its 
peculiarity  is  that,  besides  the  motion  on  its  own  axis,  it 
also  has  a  progressive  one.  Let  b  be  the  axis  of  the  pul- 
ley, and  to  it  the  weight  w  is  attached,  the  power  is  ap- 
plied at  a.  Draw  the  diameter  a  c,  then  c  is  the  fulcrum 
of  a  c,  which  is  in  reality  a  lever  of  the  third  order  in 
which  the  distance,  a  c,  of  the  power  is  twice  that,  b  c,  of 
the  weight.  Consequently  "  the  movable  pulley  doubles 

What  is  a  fixed  pulley  ?  Describe  the  nature  of  its  action.  What  is  the 
result  of  the  action  of  the  fixed  pulley  ?  What  is  a  movable  pulley  ?  To 
what  extent  does  it  increase  the  power  ? 


SYSTEMS    OF    PULLEYS. 


133 


Fig.  147. 


the  effect  of  the  power,"  and  the  dis- 
tance traversed  by  the  power  is  twice 
that  traversed  by  the  weight. 

A  movable  pulley  is  sometimes 
called  "  a  runner;"  and,  as*it  would 
be  often  inconvenient  to  apply  the 
power  in  the  upward  direction,  as  at 
a  P,  there  is  commonly  associated 
with  the  runner  a  fixed  pulley,  which, 
without  changing  the  value  of  the 
power,  enables  us  to  vary  the  direc-  c 
tion  of  its  action. 

Systems  of  pulleys  are  arrange- 
ments of  sheaves,  movable  and  fix- 
ed. 

When  one  fixed  pulley  acts  on  a  number  of  movable 
ones,    equilibrium   is    maintained,  when   the    power  and 

Fi^.  148.  Fig.  149.  Fig-.  150. 


i 


What  are  systems  of  pulleys? 


134  THE  WHEEL  AND  AXLE. 

weight  are  to  each  other  as  1  to  that  power  of  2  which 
equals  the  number  of  the  movable  pulleys.  Thus,  if 
there  be,  as  in  Fig.  148,  three  movable  pulleys,  the 
power  is  to  the  weight 

as  1  :  23  that  is  1:8; 

consequently,  on  such  a  system,  a  given  power  will  sup- 
port an  eightfold  weight. 

When  several  movable  and  fixed  pulleys  are  employed, 
as  in  Fig.  149,  equilibrium  is  obtained  when  the  power 
equals  the  weight  divided  by  twice  the  number  of  mov- 
able pulleys. 

In  such  systems  of  pulleys  there  is  a  great  loss  of  power 
arising  from  the  friction  of  the  sheaves  against  the  sides 
of  the  blocks,  and  on  their  axles.  In  White's  pulley  this 
is,  to  a  considerable  extent,  avoided.  This  contrivance 
is  represented  in  Fig.  150.  It  consists  of  several  sheaves 
of  unequal  diameters,  all  turned  on  one  common  mass, 
and  working  on  one  common  axis.  The  diameters  of  these, 
in  the  upper  blocks,  are  as  the  numbers  2,  4,  6,  &c.,  and  in 
the  lower  1,  3,  5,  &c. ;  consequently,  they  all  revolve  in 
equal  times,  and  the  rope  passes  without  sliding  or  scraping 
upon  the  grooves. 

THE    WHEEL    AND    AXLE. 

The  wheel  and  axle  consists  of  a  cylinder,  A,  Fig.  151, 
revolving  upon  an  axis,  and 
having  a  wheel,  R,  of  larger 
diameter,  immovably  affixed 
to  it.  The  power  is  applied 
to  the  circumference  of  the 
wheel,  the  weight  to  that  of 
the  axle. 

The  law  of  equilibrium  is, 
that  "  the  power  must  le  to 
the  weight  as  tlie  radius  of 
the  axle  is  to  that  of  the 
wheel" 

This  instrument  is,  evidently,  nothing  but  a  modifica- 
tion of  the  lever;  it  may  be  regarded  as  a  continuously 

Give  the  law  of  equilibrium  when  one  fixed  pulley  acts  on  a  system  of 
movable  ones.  What  is  it  when  several  movable  and  fixed  ones  are  em- 
ployed? Describe  White's  pulley  and  the  difficulties  it  avoids.  What  is 
meant  by  the  Wtleel  and  axle '[  What  is  the  law  of  its  equilibrium  ? 


THE    WHEEL    AND    AXLE. 


135 


.  152. 


acting  lever.  In  its  mode  of  action,  the  common  lever 
operates  in  an  intermitting  way,  and,  as  it  were,  by  small 
steps  at  a  time.  A  mass,  which  is  forced  up  by  a  lever  a 
short  distance,  must  be  temporarily  propped,  and  the 
lever  readjusted  before  it  can  be  brought  into  action 
again  ;  but  the  wheel  and  axle  continues  its  operation 
constantly  in  the  same  direction. 

That  this  is  its  mode  of  ac- 
tion may  be  understood  from 
considering  Fig.  152,  in  which 
let  c  be  the  common  center  of 
the  axle  c  b,  and  of  the  wheel 
c  a,  a  the  point  of  application 
of  the  power  P,  and  b  that  of 
the  weight  \V.  Draw  the  line 
a  c  b  ;  it  evidently  represents  a 
lever  of  the  first  order  of  which 
the  fulcrum  is  c,  and  from  the 
principles  of  the  lever  it  is  easy  to  demonstrate  the  law 
of  equilibrium  of  this  machine,  as  just  given.  Further,  it 
is  immaterial  in  what  direction  the  power  be  applied,  as 
P'  at  the  point  a'  for  a'  c  b  still  forms  a  bent  lever,  and 
the  same  principle  still  holds  good. 

Sometimes  the  wheel  is  Fis- 154- 
replaced  by  a  winch,  as  in 
Fig.  153,  it  is  then  called  a 
windlass,  if  the  motion  is 
vertical ;  but  if  it  be  hori- 
zontal, as  in  Fig.  154,  the 
machine  is  called  a  capstan. 

Wheels  and  axles  are  often  made  to 
act  upon  one  another  by  the  aid  of  cogs,  as  in  clockwork 
and  mill  machinery.  In  these  cases  the  cogs  on  the  pe- 
riphery of  the  wheel  take  the  name  of  teeth,  those  on  the 
axle  the  name  of  haves,  and  the  axle  itself  is  called  a 
pinion. 

The  law  of  equilibrium  of  such  machines  may  be  easily 
demonstrated  to  be,  that  the  power  multiplied  by  the  pro- 
duct of  the  number  of  teeth,  in  all  the  icheels,  is  equal  to  the 
weight  multiplied  by  the  product  of  the  number  of  leaves 
in  all  the  pinions. 

Describe  its  mode  of  action.  What  is  a  windlass  and  a  capstan  ?  What  are 
teeth,  leaves,  and  pinions  ?  What  is  the  law  of  equilibrium  of  wheelwork? 


Fi    j53 


136 


WHEELWORK. 


A  system  of  wheel  and  pinion  work  is  represented  at 

TT'.'rt.      1  K  ^  T*-    4 a    ar»or*r»£»1  \T    T>or»*>ccn  i*v 


Fig.  155. 


Fig.  155.  It  is  scarcely  necessary 
to  observe,  that  in  it,  as  in  all  other 
cases,  the  law  of  virtual  velocities 
holds  good — the  power  multiplied 
by  the  velocity  of  the  power  is 
equal  to  the  weight  multiplied  by 
the  velocity  of  the  weight. 

In  the  construction  of  such  ma- 
chinery attention  has  to  be  paid  to 
the  form  of  the  teeth,  so  that  they 
may  not  scrape  or  jolt  upon  one  another.  Several  of  them 
should  be  in  contact  at  once,  to  diminish  the  risk  of  frac- 
ture and  the  wear. 

If  the  teeth  of  a  wheel  be  in  the  direction  of  radii 
from  its  center  it  is  called  a  spur-wheel. 

If  the  teeth  are  parallel  to  the  axis  of  the  wheel  it  is 
called  a  crown-wheel. 

If  the  teeth  are  oblique  to  the  axis  of  the  wheel  it  is 
called  a  beveled-wheel. 

By  combining  these  different  forms  of  wheel  suitably 
together,  the  resulting  motion  can  be  transferred  to  any 
required  plane.  Thus,  by  a  pair  of  beveled-wheels  mo- 
tion round  a  vertical  axis  may  be  transferred  to  a  hori- 
zontal one,  or,  indeed,  one  in  any  other  direction. 

When  a  pinion  is  made  to  work  on  a  toothed-bar,  it 
constitutes  a  rack.  This  contrivance  is  under  the  same 
law  as  the  wheel  and  axle. 


What  precautions  have  to  he  used  as  respects  the  form  of  teeth  ?  What 
is  a  spur,  a  crown,  and  a  beveled-wheel  ?  How  may  motion  be  trans- 
ferred to  different  planes  ?  What  is  a  rack  ? 


THE    INCLINED    PLANE.  137 


LECTURE  XXIX. 

THE  INCLINED  PLANE. — Description  of  the  Inclined  Plane. 
— Modes  of  Applying  the  Power. —  Conditions  of  Equi- 
librium when  the  Power  is  Parallel  to  the  Plane  or  Par- 
allel to  the  Base. — Position  of  Greatest  Advantage. 

THE  WEDGE. — Description  and  Mode  of  using  it. 

THE  SCREW. — -Formation  of  the  Screw. 

BY  the  inclined  plane  we  mean  an  unyielding  plane 
surface  inclined  obliquely  to  the  resist-  Fig.  156 

ance  to  be  overcome. 

In  Fig.  156,  A  C  represents  the  inclined 
plane  ;  the  angle  at  A  is  the  elevation  of 
the  plane  ;  the  line  A  C  is  the  length,  C 
B  is  the  height,  A  B  the  base. 

In  the  inclined  plane  the  power  may 
be  applied  in  the  following  directions  : 

1.  Parallel  to  the  plane ; 

2.  Parallel  to  its  base  ; 

3.  Parallel  to  neither  of  these  lines. 

As  in  the  former  cases,  so  in  this — ^the  conditions  of 
the  equilibrium  may  be  deduced  from  those  of  the  lever. 

Let  us  take  the  first  instance,  when  the  power  is  ap- 
plied parallel  to  the  inclined  plane.  Let  Q,  Fig.  156,  be 
a  body  placed  upon  the  plane,  A  C,  the  height  of  which 
is  B  C,  and  the  base  A  B.  The  weight  of  this  body  acts 
in  the  vertical  direction,  a  W;  the  body  rests  on  the  point, 
c,  as  on  a  fulcrum  ;  and  the  power,  P,  under  the  supposi- 
tion, acts  on  Q,  in  the  direction  a  P.  From  the  fulcrum, 
c,  draw  the  perpendicular,  c  b,  to  the  line  of  direction  of 
the  weight,  a  W ;  draw  also  c  a.  Then  does  b  c  a  repre- 
sent a  bent  lever,  the  power  being  applied  to  the  point 
a,  and  the  weight  at  the  point,  b;  and,  therefore,  the 
power  is  to  the  weight  as  b  c  is  to  a  c;  but  the  triangles,  a 

Describe  the  inclined  plane.  What  is  the  angle  of  elevation,  the  length, 
the  height,  and  the  base  ?  in  how  many  directions  may  the  power  be  ap 
plied  ? 


138  THE    INCLINED    PLANE. 

I  c,  A  B  C,  are  similar  to  each  other.     Therefore,  we  ar- 
rive at  the  following  law: 

When  tlie  power  acts  in  a  direction  parallel  to  the  in- 
clined plane,  it  will  be  in  equilibria  with  the  weight  when 
it  is  to  the  weight  as  the  perpendicular  of  the  plane  is  to  its 
length. 

In  a  similar  manner  it  may  be  shown  that  when  the 
power  acts  parallel  to  the  base  it  will  be  in  equilibria  with 
the  weight,  if  it  be  to  the  weight  as  the  perpendicular  of  the 
plane  is  to  its  base. 

In  different  inclined  planes  the  power  increases  as  the 
height  of  the  plane,  compared  with  its  length,  diminishes, 
and  the  best  direction  of  action  is  parallel  to  the  inclined 
plane.  This  is  very  evident  from  the  consideration  that 
if  the  power  be  directed  above  the  plane  a  portion  of  it 
is  expended  in  lifting  the  weight  off  the  plane,  while  the 
diminished  residue  draws  it  up.  If  it  be  directed  down- 
ward a  part  is  expended  in  pressing  the  weight  upon  the 
plane,  and  the  diminished  residue  draws  it  up.  There- 
fore, if  the  power  acts  parallel  to  the  plane,  it  operates 
under  the  most  advantageous  condition. 

Fig.  157.  The  laws  of  the  inclined 

plane  may  be  illustrated  by 
an  instrument,  such  as  is  rep- 
resented in  Fig.  157,  in  which 
A  c  A'  c  is  the  plane,  which 
may  be  set  at  any  angle.  It 
works  upon  an  axis,  A  A'. 
Upon  the  plane  a  roller,  e, 
moves.  It  has  a  string  passing  over  a  pulley,  d,  and  ter- 
minating in  a  scale-pan,  f.  in  which  weights  may  be 
placed.  The  direction  of  the  string  may  be  varied,  so  as 
to  be  parallel  to  the  plane,  or  the  base,  or  any  other  di- 
rection. 

The  inclined  plane  is  used  for  a  variety  of  purposes — 
very  frequently  for  facilitating  the  movements  of  heavy 
loads. 

THE    WEDGE. 

The  wedge  may  be  regarded  as  two  inclined  planes 


What  is  the  law  of  equilibrium  when  the  power  acts  parallel  to  the 
plane?  What  is  it  when  the  power  acts  parallel  to  the  hase  .'  For  what 
purposes  is  the  inclined  plane  used  ?  Describe  the  wedge. 


THE    WEDGE. 


139 


Kg.  158. 
A 


\ 


laid  base  to  base — A  C  D  being  one,  and 
A  B  D  being  the  other.  The  planes  B  D 
and  C  D  constitute  the  sides  or  faces  of  the 
wedge  ;  B  C  is  its  back,  and  A  D  its  length. 
The  mode  of  employing  the  wedge  is  not 
by  the  agency  of  pressure,  but  of  percus- 
sion. Its  edge  being  inserted  into  a  fissure, 
the  wedge  is  driven  in  by  blows  upon  its 
back.  It  is  kept  from  recoiling  by  the  fric- 
tion of  its  sides  against  the  surfaces  past  which  it  Fig.  159. 
has  been  forced. 

This  mode  of  application  of  the  wedge  prevents 
us  from  comparing  its  theory  with  that  of  the  in- 
clined plane — a  power  to  which  it  has  so  much 
Fig.  161.         external  resemblance. 

The  power  of  the  wedge  in- 
creases as  the  length  of  its  back, 
compared  with  that  of  its  sides,  is  dimin- 
ished. As  instances  of  its  application,  we 
may  mention  the  splitting  of  timber,  the 
raising  of  heavy  weights,  such  as  ships. 
Different  cutting-instruments,  as  chisels, 
&c.,  act  in  consequence  of  their  wedge- 
shaped  form. 

THE    SCREW. 

If  we  take  a  piece  of  paper  cut  into  a 
long,  right-angled  triangle,  Fig.  160,  and 
wind  it  about  a  cylinder  Fig.  161,  so  that 
the  height  C  B  of  the  triangle  is  parallel 
to  the  axis,  the  length  A  C  will  trace  a 
screw-line  on  the  surface.  The  same  re- 
sults if  we  take  a  cylinder  and  wind  upon 
it  a  flexible  cord,  so  that  the  strands  of  the 
cord  uniformly  touch  one  another. 

In   any  screw,   the  line   which  is  thus 
traced  upon  the  cylinder  goes  under  the 
name  of  the  "worm,"  or  "thread,"  and 
A  each  complete  turn  that  it  makes  is  called 


Fig.  160, 


On  what  principle  does  it  act  ?    On  what  does  its  power  depend  ?    How 
may  a  screw-thread  be  represented  1 


140  THE    SCREW. 

"  a  spire."  The  distance  from  one  thread  to  another, 
which,  of  course,  must  be  perfectly  uniform  throughout 
the  screw,  is  called  the  breadth  of  the  worm. 

In  most  cases  the  screw  requires  a  corresponding 
cavity  in  which  it  may  work;  this  passes  under  the 
name  of  "  a  nut."  Sometimes  the  nut  is  caused  to 
move  upon  the  screw,  and  sometimes  the  screw  in 
the  nut.  In  either  case  the  movable  part  requires  a 
lever  to  be  attached,  to  the  end  of  which  the  power  is 
applied. 

The  law  of  equilibrium  of  the  screw  is,  that  "  the 
power  is  to  the  weight  as  the  breadth  of  the  worm  is  to  the 
circumference  described  by  that  point  of  the  lever  to  which 
the  power  is  attached. 

When  the  end  of  the  screw  is  advancing  through  a 
nut,  this  law  evidently  becomes  that  the  power  is  to  the 
weight  as  the  circumference  described  by  the  power  is  to  the 
space  through  which  the  end  of  the  screw  advances.  It  is 
obvious,  therefore,  that  the  force  of  the  screw  increases 
as  its  threads  are  finer,  and  as  the  lever  by  which  it  is 
urged  is  longer. 

When  the  thread  of  a  screw  works  in  the  teeth  of  a 
Fig  162.  wheel,   as  shown    in  Fig.  162,   it 

constitutes  an  endless  screw.  An 
important  use  of  this  contrivance 
is  in  the  engine  for  dividing  grad- 
uated circles.  The  screw  is  also 
used  to  produce  slow  motions,  or  to 
measure  by  the  advance  of  its  point, 
minute  spaces.  In  the  spherome- 
ter,  represented  in  Fig.  5,  we  have  an  example  of  its 
use. 

For  all  these  purposes  where  slow  motions  have  to  be 
given,  or  minute  spaces  divided,  the  efficacy  of  the  screw 
will  increase  with  the  closeness  of  its  thread.  But  there 
is  soon  a  practical  limit  attained ;  for,  if  the  thread  be  too 
fine  it  is  liable  to  be  torn  off.  To  avoid  this,  and  to  attain 
those  objects  almost  to  an  unlimited  extent,  Hunter's 
screw  is  often  used.  It  may  be  understood  from  Fig. 
163.  It  consists  of  a  screw,  A,  working  in  a  nut,  C. 

What  is  the  worm  and  the  spire  ?  What  is  a  nut  ?  What  is  the  law  of 
equilibrium  of  the  screw?  When  the  end  of  the  screw  advances  what 
does  this  law  become  ?  Describe  an  endless  screw. 


PASSIVE    FORCES. 


To  a  movable  piece,  D,  a  second 
screw,  B,  is  affixed.  This  screw 
works  in  the  interior  of  A,  which 
is  hollow,  and  in  which  a  corre- 
sponding thread  is  cut.  While, 
therefore,  A  is  screwed  down- 
ward, the  threads  of  B  pass  up- 
ward, and  the  movable  piece,  D, 
advances  through  a  space  which 
is  equal  to  the  difference  of  the 
breadth  of  the  two  screws.  In 
this  way  very  slow  or  minute 
motions  may  be  obtained  with  a 
screw,  the  threads  of  which  are 
coarse. 


141 


Fig.  163. 


LECTURE  XXX. 

OF  PASSIVE  OR  RESISTING  FORCES. — Difference  'between 
the  Theoretical  and  Actual  Results  of  Machinery. — Of 
Impediments  to  Motion. — Friction. — Sliding  and  Roll- 
ing Friction. — Coefficient  of  Friction. — Action  of  Un- 
guents.— Resistance  of  Media. — General  Phenomena  of 
Resistance. — Rigidity  of  Cordage. 

IT  has  already  been  stated,  in  the  foregoing  Lectures, 
that  the  properties  of  machinery  are  described  without 
taking  into  account  any  of  those  resisting  agencies  which 
so  greatly  complicate  their  action.  The  results  of  the 
theoiy  of  a  machine  in  this  respect  differ  very  widely  from 
its  practical  operation.  There  are  resisting  forces  or 
impeding  agencies  which  have  thus  far  been  kept  out  of 
view.  We  have  described  levers  as  being  inflexible,  the 
cords  of  pulleys  as  perfectly  pliable,  and  machinery,  gen- 
erally, as  experiencing  no  friction.  In  the  case  of  one  of 
the  powers,  it  is  true  that  this  latter  resisting  force  must 
necessarily  be  taken  into  account ;  for  it  is  upon  it  that 
the  efficacy  of  the  wedge  chiefly  depends. 

Describe  Hunter's  screw.  What  is  meant  by  passive  or  resisting  forces  ? 
Why  does  the  theoretical  action  of  a  machine  differ  from  its  practical 
operation  ? 


142  FRICTION. 

So,  too,  in  speaking  of  the  motion  of  projectiles,  it  has 
been  stated  that  the  parabolic  theory  is  wholly  departed 
from,  by  reason  of  the  resistance  of  the  air;  and  that  not 
only  is  the  path  of  such  bodies  changed,  but  their  range 
becomes  vastly  less  than  what,  upon  that  theory,  it  should 
be.  Thus,  a  24-pound  shot,  discharged  at  an  elevation 
of  45°,  with  a  velocity  of  2000  feet  per  second,  would 
range  a  horizontal  distance  of  125,000  feet  were  it  not 
for  the  resistance  of  the  air ;  but  through  that  resistance 
its  range  is  limited  to  about  7300  feet. 

Of  these  impediments  to  motion  or  passive  or  resisting 
forces,  three  leading  ones  may  be  mentioned.  They  are, 
1st,  friction;  2d,  resistance  of  the  media  moved  through  ; 
3d,  rigidity  of  cordage. 

OF  FRICTION. 

Friction  arises  from  the  adhesion  of  surfaces  brought 
into  contact,  and  is  of  different  kinds — as  sliding  friction, 
when  one  surface  moves  parallel  to  the  other,  rolling 
friction,  when  a  round  body  turns  upon  the  surface  of 
another. 

By  the  measure  of  friction,  we  mean  that  part  of  the 
weight  of  the  moving  body  which  must  be  expended  in 
overcoming  the  friction.  The  fraction  which  expresses 
this  is  termed  the  coefficient  of  friction.  Thus,  the  coef- 
ficient of  sliding  friction  in  the  case  of  hard  bodies,  and 
when  the  weight  is  small,  ranges  from  one  seventh  to  one 
third. 

It  has  been  proved  by  experiment  that  friction  increases 
as  the  weight  or  pressure  increases,  and  as  the  surfaces 
in  contact  are  more  extensive,  and  as  the  roughness  is 
greater.  With  surfaces  of  the  same  material  it  is  nearly 
proportional  to  the  pressure.  The  time  which  the  sur- 
faces have  been  in  contact  appears  to  have  a  considerable 
influence,  though  this  differs  much  with  surfaces  of  differ- 
ent kinds.  As  a  general  rule,  similar  substances  give  rise 
to  greater  friction  than  dissimilar  ones. 

On  the  contrary,  friction  diminishes  as  the  pressure  is 

Give  an  illustration  of  resisting  force  in  the  case  of  projectiles.  How 
many  of  these  impediments  may  be  enumerated  ?  What  varieties  of  fric- 
tion are  there  ?  What  is  the  coefficient  of  friction  ?  Mention  some  of  the 
conditions  which  increase  friction. 


RESISTANCE    OF    MEDIA.  143 

less,  as  the  polish  of  the  moving  surfaces  is  more  perfect, 
and  as  the  surfaces  in  contact  are  smaller.  It  may  also 
be  diminished  by  anointing  the  surfaces  with  some  suita- 
ble unguent  or  greasy  material.  Among  such  substances 
as  are  commonly  used  are  the  different  fats,  tar,  and  black 
lead.  By  such  means,  friction  may  be  reduced  to  one 
fourth. 

Of  the  friction  produced  by  sliding  and  rolling  motions, 
the  latter,  under  similar  circumstances,  is  far  the  least. 
This  partly  arises  from  the  fact  that  the  surfaces  in  con- 
tact constitute  a  mere  line,  and  partly  because  the  asperi- 
ties are  not  abraded  or  pushed  aside  before  motion  can 
ensue.  The  nature  of  this  distinction  may  be  clearly  un- 
derstood by  observing  what  takes  place  when  two  brushes 
with  stiff  bristles  are  moved  over  one  another,  and  when 
a  round  brush  is  rolled  over  a  flat  one.  In  this  instance, 
the  rolling  motion  lifts  the  resisting  surfaces  from  one 
another ;  in  the  former,  they  require  to  be  forcibly  pushed 
apart. 

Though,  in  many  instances,  friction  acts  as  a  resisting 
agency,  and  diminishes  the  power  we  apply  to  machines, 
in  some  cases  its  effects  are  of  the  utmost  value.  Thus, 
when  nails  or  screws  are  driven  into  bodies,  with  a  view 
of  holding  them  together,  it  is  friction  alone  which  main- 
tains them  in  their  places.  The  case  is  precisely  the 
same  as  in  the  action  of  a  wedge. 

RESISTANCE   OF  MEDIA. 

A  great  many  results  in  natural  philosophy  illustrate 
the  resistance  which  media  offer  to  the  passage  of  bodies 
through  them.  The  experiment  known  under  the  name 
of  the  guinea  and  feather  experiment  establishes  this  for 
atmospheric  air.  In  a  very  tall  air-pump  receiver  there 
are  suspended  a  piece  of  coin  and  a  feather  in  such  a  way 
that,  by  turning  a  button,  at  a,  Fig.  164,  the  piece  on 
which  they  rest  drops,  and  permits  them  to  fall  to  the 
pump-plate.  Now,  if  the  receiver  be  full  of  atmospheric 
air,  on  letting  the  objects  fall,  it  will  be  found  that,  while 
the  coin  descends  with  rapidity,  and  reaches,  in  an  instant, 

Mention  some  that  diminish  it.  What  is  the  difference  of  effect  be- 
tween sliding  and  rolling  friction?  Give  an  illustration  of  this.  Under 
what  circumstances  does  advantage  arise  from  friction  ? 


144 


RESISTANCE     OF    MEDIA. 


the  pump-plate,  the  feather  comes  down 
leisurely,  being  buoyed  up  by  the  air,  and 
the  speed  of  its  motion  resisted.  But  if  the 
air  is  first  extracted  by  the  pump,  and  the 
objects  allowed  to  fall  in  vacuo,  both  pre- 
cipitate themselves  simultaneously  with  equal 
vel°city>  ai)d  accomplish  their  fall  in  equal 
times. 

In  the  vibrations  of  a  pendulum,  the  final 
stoppage  is  due  partly  to  friction  and  partly 
to  this  cause.  And  in  the  case  of  motions 
taking  place  in  water,  we  should,  of  course, 
expect  to  find  a  greater  resistance  arising 
from  the  greater  density  of  that  liquid. 

The  resisting  force  of  a  medium  depends  up- 
on its  density,  upon  the  surface  which  the  mov- 
ing body  presents,  and  on  the  velocity  with  which  it  moves. 
Water,  which  is  800  times  more  dense  than  air,  will 
offer  a  resistance  800  times  greater  to  a  given  motion. 
Of  the  two  mills  represented  in  Fig.  36,  that  which  goes 
with  its  edge  first  runs  far  longer  than  that  which  moves 
with  its  plane  first.  We  are  not,  however,  to  understand 
that  the  eifect  of  the  medium,  on  a  body  moving  through 
it,  increases  directly  as  the  transverse  section  of  the  bodv; 
for  a  great  deal  depends  upon  its  figure.  A  wedge,  going 
with  its  edge  first,  will  pass  through  water  more  easily 
than  if  impelled  with  its  back  first,  though,  in  both  in- 
stances, the  area  of  the  transverse  section  is  of  course  the 
same.  It  is  stated  that  spherical  balls  encounter  one 
fourth  less  resistance  from  the  air  than  would  cylinders 
of  equal  diameter;  and  it  is  upon  this  principle  that  the 
bodies  of  fishes  and  birds  are  shaped,  to  enable  them  to 
move  with  as  little  resistance  as  may  be  through  the  me- 
dia they  inhabit. 

The  resistance  of  a  medium  increases  with  the  velocity 
with  which  a  body  moves  through  it,  being  as  the  square 
of  the  velocity,  so  long  as  the  motion  is  not  too  rapid  ;  but 
when  a  high  velocity  is  reached,  other  causes  come  into 
operation,  and  disturb  the  result. 

Describe  the  guinea  and  feather  experiment.  What  does  it  prove? 
What  is  the  cause  of  the  stoppage  of  a  pendulum  ?  How  does  the  density 
of  a  liquid  affect  its  resistance  ?  How  is  resistance  affected  by  figure  ? 
How  by  velocity? 


RIGIDITY    OF    CORDAGE.  145 

As  with  friction,  so  with  the  resistande  of  media,  a 
great  many  results  depend  on  this  impediment  to  mo- 
tion ;  among  such  may  be  mentioned  the  swimming  of 
fish  through  water,  and  the  flight  of  birds  through  the 
air.  It  is  the  resistance  of  the  air  which  makes  the  para- 
chute descend  with  moderate  velocity  downward,  and 
causes  the  rocket  to  rise  swiftly  upward. 


RIGIDITY    OF    CORDAGE. 

In  the  action  of  pulleys,  in  machinery  in  which  the  use  of 
cordage  is  involved,  the  rigidity  of 
that  cordage  is  an  impediment  to 
motion.  When  a  cord  acts  round 
a  pulley,  in  consequence  of  imper- 
fect flexibility,  it  obtains  a  leverage 
on  the  pulley,  as  may  be  under- 
stood from  Fig.  165,  in  which  let 
C  K  D  be  the  pulley  working  on  a 
pivot  at  O  ;  let  A  and  B  be  weights 
suspended  by  the  rope  A  C  K  D  B. 
From  what  has  been  said  respect- 
ing the  theory  of  the  pulley,  the 
action  of  the  machine  may  be  regarded  as  that  of  a  lever, 
COD,  with  equal  arms,  CO,  O  D.  Now,  if  the  cord 
were  perfectly  inflexible,  on  making  the  weight  A  descend 
by  the  addition  of  a  small  weight  to  it,  it  would  take  the 
position  at  A',  the  rope  being  a  tangent  to  the  pulley  at 
C' ;  at  the  same  time  B,  ascending,  would  take  the  position 
B',  its  cord  being  a  tangent  at  D'.  From  the  new  posi- 
tions, A'  and  B',  which  the  inflexible  cord  is  thus  sup- 
posed to  have  assumed,  draw  the  perpendiculars,  A7  E, 
B'  F.,  then  will  O  E,  O  F,  represent  the  arms  of  the  lever 
on  which  they  act — a  diminished  leverage  on  the,  side  of 
the  descending,  and  an  increased  leverage  on  the  side  of 
the  ascending  weight  is  the  result. 

In  practice  the  result  does  not  entirely  conform  to  the 
foregoing  imaginary  case,  because  cords  are,  to  a  certain 
extent,  flexible.  As  their  pliability  diminishes,  the  dis- 
turbing effect  is  greater.  The  degree  of  inflexibility  de- 


Mention  some  of  the  valuable  results  which  depend  on  it.  Give  a  general 
lage 

O 

G 


idea  of  the  action  of  rigidity  of  cordage     What  takes  place  in  case  of  ab- 
solute inflexibility,  as  in  Fig.  165?    On  what  does  inflexibility  depend  ? 


146  RIGIDITY    OF    CORDAGE. 

pends  on  many  casual  circumstances,  such  as  dampness 
or  dryness,  or  the  nature  of  the  substance  of  which  they 
are  made.  Inflexibility  increases  with  the  diameter  of  a 
cord,  and  with  the  smallness  of  the  pulley  over  which  it 
runs. 


UNDULATIONS.  147 


OF  UNDULATORY  MOTIONS. 


LECTURE  XXXI. 

OF  UNDULATIONS. — Origin  of  Undulations. — Progressive 
and  stationary  Undulation. — Course  of  a  progressive 
Wave. — Nodal  Points. —  Three  different  kinds  of  Vibra- 
tion.—  Transverse  Vibration  of  a  Cord. —  Vibrations  of 
Rods.  —  Vibrations  of  elastic  Planes.  —  Vibrations  of 
Liquids. —  Waves  on  Water. 

WHEN  an  elastic  body  is  disturbed  at  any  point,  its 
particles  gradually  return  to  a  position  of  rest,  after  exe- 
cuting a  series  of  vibratory  movements.  Thus,  when  a 
glass  tumbler  is  struck  by  a  hard  body,  a  tremulous  mo- 
tion is  communicated  to  its  mass,  which  gradually  declines 
in  force  until  the  movement  finally  ceases. 

In  the  same  manner  a  stretched  cord,  which  is  drawn 
aside  at  one  point,  and  then  suffered  to  go,  is  thrown  into 
a  vibratory  or  undulatory  movement ;  and,  according  as 
circumstances  differ,  two  different  kinds  of  undulation 
may  be  established,  1st,  progressive  undulations ;  2d,  sta- 
tionary undulations.  % 

In    progressive  un                             Fig.  166. 
dulations    the    vibra- 
ting particles  of  a  body 
communicate  their  mo- 
tion  to    the    adjacent  JLm ^ •^*~>        e 

particles ;     a    succes- 
sive   propagation    of <  ^ 

movement,  therefore,  ~ "G 

ensues.      Thus,   if   a 

cord  is  fastened  at  one    Wm.  ^^^^^ sg 

end,  and  the  other  is 

moved  up  and  down,   ym.     **"*  ^ ^ e 

a  wave  or  undulation, 

m  D  n  E  o,  is  produced.     The  part,  m  D  nt  is  the  elevation 

Under  what  circumstances  do  vibratory  movements  arise?  How  many- 
kinds  of  undulations  are  there  ?  Describe  the  nature  of  a  progressive  un- 
dulation. 


148 


KINDS    OF    VIBRATIONS. 


of  the  wave,  D  being  the  summit,  n  E  o  is  the  depression, 
E  being  the  lowest  point,  D  p  is  the  height,  q  E  the  depth, 
and  m  o  the  length  of  the  wave. 

But,  under  the  circumstances  here  considered,  the  mo- 
ment this  wave  has  formed,  it  passes  onward,  and  suc- 
cessively assumes   the   positions   indicated  at  I,  II,  III. 
When  it  has  arrived  at  the  other  end  of  the  cord,  it  at 
once  returns  with  an  inverted  motion,  as  shown  at  IV 
and  V.     This,  therefore,  is  a  progressive  undulation. 
Again,  instead  of  the  cord  receiving  one  impulse,  let  it 
Fig.  167.  be  agitated  equally  at  equal  inter- 

vals of  time;  it  will  then  divide  itself, 
as  shown  in  Fig.  167,  into  equal 
elevations  and  depressions  with  in- 
tervening points,  m  n,  which  are  at  rest.  These  are  sta- 
tionary undulations,  and  the  points  are  called  nodal  points. 
The  agents  by  which  undulatory  movements  are  estab- 
lished are  chiefly  elasticity  and  gravity.  It  is  the  elas- 
ticity of  air  which  enables  it  to  transmit  the  vibratory 
motions  which  constitute  sound,  and,  for  the  same  reason, 
steel  rods  and  plates  of  glass  may  be  thrown  into  musical 
vibrations.  In  the  case  of  threads  and  wires,  a  sufficient 
degree  of  elasticity  may  be  given  by  forcibly  stretching 
them.  Waves  on  the  surface  of  liquids  are  produced  by 
the  agency  of  gravity. 

There  are  three  different  kinds  of  vibrations  into  which 
a  stretched  string  may  be  thrown  : 
transverse,  longitudinal,  and  twisted. 
These  may  be  illustrated  by  the  in- 
strument represented  at  Fig.  168. 
It  consists  of  a  piece  of  spirally- 
twisted  wire,  stretched  from  a  frame 
by  a  weight.  If  the  lower  end  of  the 
wire  be  secured  by  a  clamp,  on  pull- 
ing the  wire  in  the  middle,  and  then 
letting  it  go,  it  executes  transverse 
vibrations.  If  the  weight  be  gently 
lifted,  and  then  let  fall,  the  wire  per- 
forms longitudinal  vibrations ;  and  if 

What  is  meant  by  the  height,  depth,  and  length  of  a  wave  '/  Describe 
the  stationary  vibration.  By  what  agents  are  undulatory  motions  estab- 
lished ?  How  may  elasticity  be  communicated  to  cords?  Into  how 
many  kinds  of  vibration  may  a  string  be  thrown  ?  How  may  this  be  illus- 
trated by  the  apparatus  represented  in  Fig.  168  ? 


Fig.  168. 


TRANSVERSE    VIBRATIONS.  149 

the  weight  be  twisted  round,  and  then  released,  we  have 
rotatory  vibrations. 

If  we  take  astring,  a  b,  Fig.I69,  and  having  stretched  it  be- 
tween two  fixed  points,  a  Fi    169 
and  b,  draw  it  aside,  and 
then  let  it  go,  it  executes            ^ — 
transverse  vibrations,  as  a<^T 
has    already    been    de- 
scribed.    The  cause  of 

its  motion,  from  the  position  we  have  stretched  it  to,  is  its 
own  elasticity.  This  makes  it  return  from  the  position, 
a  c  b,  to  the  straight  line,  afb,  with  a  continually  accel- 
erated velocity  ;  but  when  it  has  arrived  in  afb,  it  cannot 
stop  there,  its  momentum  carrying  it  forward  to  a  d  b,  with 
a  velocity  continually  decreasing.  Arrived  in  this  position, 
it  is,  for  a  moment,  at  rest ;  but  its  elasticity  again  impels 
it  as  before,  but  in  the  reverse  direction  to  afb;  and  so 
it  executes  vibrations  on  each  side  of  that  straight  line 
until  it  is  finally  brought  to  rest  by  the  resistance  of  the 
air.  One  complete  movement,  from  a  c  b  to  a  d  b  and 
back,  is  called  a  vibration,  and  the  time  occupied  in  per- 
forming it  the  time  of  an  oscillation. 

The  vibratory  movements  of  such  a  solid  are  isochro- 
nous, or  performed  in  equal  lines.  They  increase  in 
rapidity  with  the  tension — that  is,  with  the  elasticity — 
being  as  the  square  root  of  that  force.  The  number  of 
vibrations  in  a  given  time  is  inversely  as  the  length  of  the 
string,  and  also  inversely  as  its  diameter. 

The  vibrations  of  solid  bodies  may  be  studied  best  un- 
der the  divisions  of  cords,  rods,  planes,  and  masses.  The 
laws  of  the  vibrations  of  the  first  are  such  as  we  have  just 
explained. 

In  rods  the  transverse  vibrations  are  isochronous,  and  in 
a  given  time  are  in  number  inversely  as  the  squares  of  the 
lengths  of  the  vibrating  parts.  Thus,  if  a  rod  makes  two 
vibrations  in  one  second,  if  its  length  be  reduced  to  half 
it  will  make  four  times  as  many — that  is,  eight ;  if  to  one 
fourth,  sixteen  times  as  many — that  is,  thirty-two,  &c. 
The  motion  performed  by  vibrating-rods  is  often  very  corn- 
Describe  the  transverse  vibration  of  a  string.  What  is  a  vibration? 
What  is  the  time  of  an  oscillation  ?  What  is  meant  by  isochronous  vibra- 
tions ?  How  are  the  vibrations  of  solid  bodies  divided  ?  What  are  the 
laws  for  the  vibrations  of  rods  ? 


150 


VIBRATIONS    OF    PLANES. 


Fig  170.  plex.  Thus,  if  a  bead  be  fastened  on  the  free  ex- 
tremity  of  a  vibrating  steel  rod,  Fig.  170,  it  will 
exhibit  in  its  motions  a  curved  path,  as  is  seen  at 
c.  Rods  may  be  made  to  exhibit  nodal  points. 
The  space  between  the  free  extremity  and  the  first 
nodal  point  is  equal  to  half  the  length  contained 
between  any  two  nodal  points,  but  it  vibrates  with 
the  same  velocity.  Thus,  a,  Fig.  171,  being  the 
fixed,  and  b  the  free  end  Fig.  rri. 

of  such  a  rod,  the  part 
L~~~*'    between  b  and  c  is  half  a 
the  distance,  c  c'. 

When  elastic  planes  vibrate  they  exhibit  nodal  lines, 
answering  to  the  nodal  points  in  linear  vibrations ;  and  if 
the  plane  were  supposed  to  be  made  up  of  a  series  of 
rods,  these  lines  would  answer  to  their  nodal  points.  By 
them  the  plane  is  divided  into  spaces — the  adjacent  ones 
being  always  in  opposite  phases  of  vibrations,  as  shown 
Fig- 172.  by  the  signs  +  and  -7—  in  Fig. 

172,  where  A  B  is  the  vibrating 
plane.    The  dimensions  of  these 
a  spaces  are  regulated  in  the  same 
B  way  as  the  internodes  of  vibra- 
ting-rods — that  is,  the   outside 
ones,  a  b  a  b,  are  always  half 
the  size  of  the   interior.     The 
relation   of  these    spaces,    and 
positions  of  the  nodal  lines  may 
be  determined  by  making  a  glass 
plate  covered  with  dry  sand  vibrate. 

When  the  surface  of  a  liquid,  as  water,  is  touched,  a 
wave  arises  at  the  disturbed  point,  and  propagates  itself 
into  the  unmoved  spaces  around,  continually  enlarging  as 
it  goes,  and  forming  a  progressive  undulation. 

A  number  of  familiar  facts  prove  that  the  apparent  ad- 
vancing motion  of  the  liquid  on  which  waves  are  passing 
is  only  a  deception.  Light  pieces  of  wood  are  not  hur- 
ried forward  on  the  surface  of  water,  but  merely  rise  up 
and  sink  down  alternately  as  the  waves  pass.  The  true 

What  are  they  for  elastic  planes  ?  How  may  the  nodal  lines  be  made 
visible  m  the  latter  case  ?  How  are  waves  on  liquid  surfaces  formed  ? 
Under,  such  circumstances  does  the  liquid  actually  advance,  or  is  it  sta- 


WAVES    ON    WATER.  151 

nature  of  the  motion  is  such  that  each  particle,  at  the  sur- 
face of  the  undulating  liquid,  describes  a  circle  in  a  verti- 
cal plane,  and  in  the  direction  in  which  the  wave  is  ad- 
vancing, the  movement  being  propagated  from  each  to  its 
next  neighbor,  and  so  on.  And  as  a  certain  time  must 
elapse  for  this  transmission  of  motion,  the  different  parti- 
cles will  be  describing  different  points  of  their  circu^r 
movement  at  the  same  moment.  Some  will  be  at  the 
highest  part  of  their  vertical  circle  when  others  are  in  an 
intermediate  position,  and  others  at  the  lowest,  giving  rise 
to  a  wave,  which  advances  a  distance  equal  to  its  own 
length,  while  each  particle  performs  one  entire  revolu- 
tion. Thus,  in  Fig.  173,  let  there  be  eight  particles  of 

Fig.  173. 


water  on  the  surface,  a  m,  which,  by  some  appropriate  dis- 
turbance, are  made  to  describe  the  vertical  circles  repre- 
sented at  a  b  c  d  e  f  g  //,  moving  in  the  direction  repre- 
sented by  the  darts,  and  let  each  one  of  these  commence 
its  motion  one  eighth  of  a  revolution  later  than  the  one 
before  it.  Then,  at  any  given  moment,  when  the  first  one, 
a,  is  in  the  position  marked  a,  the  second,  b,  will  be  in  the 
position  marked  7,  c  at  6,  d  at  5,  e  at  4,y  at  3,  g  at  2,  h  at 
1 ;  but  m  will  not  yet  have  begun  to  move.  If,  therefore, 
we  connect  these  various  points,  #7654321  w,  together 
by  a  line,  that  line  will  be  on  the  surface  of  the  wave,  the 
length  of  which  is  a  m,  the  height  or  depth  of  which  is 
equal  to  the  radius  of  the  circle  of  each  particle's  revolu- 
tion, and  the  time  of  passage  through  the  length  of  one 
wave  will  be  equal  to  the  time  of  the  revolution  of  each 
particle. 

What  is  the  true  nature  of  the  motion  ?    Describe  the  illustration, 
Fig.  173. 


152  REFLEXION    OF    WAVES. 


LECTURE  XXXII. 

UNDULATIONS  (continued). — Law  of  the  Reflection  of 
Undulations. — Applied  in  the  case  of  a  Plane ,  a  Circle, 
•an  Ellipse,  a  Parabola. — Case  of  a  Circular  Wave  on 
a  Plane. — Interference  of  Waves. —  Inflexion  of  Waves. 
— Intensity  of  Waves. — Method  of  Combining  Systems 
of  Waves. 

BY  a  ray  of  undulation  we  mean  a  line  drawn  from  the 
origin  of  a  wave  in  the  direction  in  which  any  given  point 
of  it  is  advancing.  A  wave  is  said  to  be  incident  when 
it  falls  on  some  resisting  surface,  and  reflected  when  it 
recoils  from  it.  Incident  rays  are  those  drawn  from  the 
origin  toward  the  resisting  surface,  and  reflected  rays 
those  expressing  the  path  of  the  undulating  points  after 
their  recoil.  The  angle  of  incidence  is  the  angle  which 
an  incident  wave  makes  with  a  perpendicular  drawn  to 
the  surface  of  impact ;  the  angle  of  reflexion  is  the  angle 
Fig.  174.  made  by  the  reflected  ray  and  the  same  per- 
b  /a  pendicular.  Thus,  let  c  be  a  resisting  sur- 
iace  of  any  kind,  a  c  an  incident  ray,  c  b 
f'  a  perpendicular  to  the  point  of  impact  of 
the  wave,  c  d  the  reflected  ray.  Then  a  c  b 
is  the  angle  of  incidence,  and  deb  the  angle 
of  reflexion. 

The  general  law  for  the  reflexion  of  waves  is,  that  "  all 
the  points  in  a  wave  will  be  reflected  from  the  surface  of 
the  solid  under  the  same  angle  at  which  they  struck  it." 

If,  therefore,  parallel  rays  fall  on  a  plane  surface,  they 
will  be  reflected  parallel ;  if  diverging,  they  will  be  re- 
flected diverging;  and  if  converging,  converging. 

If  a  circular  wave  advances  from  the  center  of  a  cir- 
cular vessel,  each  ray  falls  perpendicularly  on  the  surface 
of  the  vessel,  and  is  reflected  perpendicularly — that  is  to 
say,  back  in  the  line  along  which  it  came.  The  waves, 

What  is  meant  by  a  ray  of  undulation  ?  What  by  incident  and  reflected 
rays  ?  What  is  the  angle  of  incidence,  and  what  that  of  reflexion  ?  What 
is  the  law  of  reflexion  ?  How  does  this  apply  in  the  case  of  plane  sur- 
faces ?  What  is  the  path  of  circular  waves  advancing  from  the  center  of 
a  circular  vessel  after  reflexion  ? 


REFLEXION    OF    WAVES. 


153 


Fig. 


Fig.  176. 


therefore,  all  return  to  the  center  from  which  they  origi- 
nated. 

If  undulations  proceed  from    one  focus   of  an  ellipse, 
they  will,  after  reflection,  converge  to  the  other  focus. 

If  a  surface  be  a  parabola,  rays 
diverging  from  its  focal  point,  a, 
will,  after  reflexion,  pass  in  par- 
allel lines,  b  d]  c  d,  e  d.  Or  if 
the  rays  impinge  in  parallel  lines, 
they  will,  after  reflexion,  con- 
verge to  the  focus. 

When  diverging  rays  of  a  cir- 
cular wave  fall  upon  a  plane  surface,  their  path,  after  re- 
flexion is  such  as  it  would  have  been  had  they  originated 
from  a  point  on  the  opposite  side  of  the  plane,  and  as  far 
distant  as  the  point  of  origin  itself.  Thus,  let  c  be  the 
origin  of  a  circular  wave, 
d  a  g,  which  impinges 
on  a  plane,  ef,  after  re- 
flexion this  wave  will  be 
found  at  e  kf,  as  though 
it  had  originated  at  c',  a 
point  on  the  opposite  side 
of  ef,  as  far  as  c,  in  front 
of  it.  Now,  the  parts  of 
the  circular  wave,  dag, 
do  not  all  impinge  on  the 
plane  at  the  same  time, 
but  that  at  a,  which 
falls  perpendicularly,  im- 
pinges first,  and  is  first  reflected ;  the  ray  at  d  has  to  go 
still  through  the  distance,  d  e,  before  reflexion  takes 
place;  but,  in  this  space  of  time,  the  ray  at  a  will  have 
returned  back  to  k;  and,  in  the  same  way,  it  may  be 
shown  that  the  intermediate  rays  will  have  returned  to 
intermediate  positions,  and  be  found  in  the  line  e  k  f, 
symmetrically  situated,  with  respect  to  the  line  e  n  f,  in 
which  they  would  have  been  had  they  not  fallen  on  the 
plane.  And  it  further  follows  that  the  center,  c',  of  the 
circular  wave,  e  kf,  is  as  far  from  ef  as  is  the  centre,  c, 
of  the  circular  wave,  e  nf,  but  on  the  opposite  side. 

How  are  rays  reflected  that  come  from  one  of  the  foci  of  an  ellipse  ?  How 
is  it  in  the  case  of  a  parabola.  What  is  the  principle  illustrated  in  Fig,  176  ? 


154  INTERFERENCE    AND    INFLEXION. 

By  interference  we  mean  that  two  or  more  waves  have 
encountered  one  another,  under  such  circumstances  as  to 
destroy  each  other's  effect.  If  on  water  two  elevations 
or  two  depressions  coincide,  they  conspire ;  but  when  an 
elevation  coincides  with  a  depression,  interference  takes 
place,  arid  the  surface  of  the  fluid  remains  plane.  Waves 
which  have  thus  crossed  one  another  continue  their  mo- 
tion unimpaired. 

If  two  systems  of  waves  of  the  same  length  encounter 
each  other,  after  having  come  through  paths  of  equal 
length,  they  will  not  interfere ;  nor  will  they  interfere, 
even  though  there  be  a  difference  in  the  length  of  their 
paths,  provided  that  difference  be  equal  to  one  whole  wave, 
or  two,  or  three,  &c. 

But  if  two  systems  of  waves  of  equal  length  encounter 
each  other  after  having  come  through  paths  of  unequal 
length,  they  will  interfere,  and  that  interference  will  be 
complete  when  the  difference  of  the  paths  through  which 
they  have  come  is  half  a  wave,  or  one  and  a  half,  two 
and  a  half,  three  and  a  half,  &c. 

When  a  circular  wave  impinges  on  a  solid  in  which 
Fig.  177.  there  is  an  opening,  as  at  a,  b,  Fig. 

177,  the  wave  passes  through,  and  is 
propagated  to  the  spaces  beyond ; 
but  other  waves  arise  from  a  b,  as 
centers,  and  are  propagated  as  repre- 
sented at  c  d  e  f.  This  is  the  in- 
flexion of  waves,  and  these  new 
waves  intersecting  one  another  and 
the  primitive  one,  give  rise  to  inter- 
ferences. 

We  have  now  traced  the  chief  phenomena  of  vibrations 
in  solids  and  on  the  surface  of  liquids.  It  remains  to  do 
the  same  for  elastic  bodies,  such  as  gases. 

When  any  vibratory  movement  takes  place  in  atmos- 
pheric air,  the  impulse  communicated  to  the  particles 
causes  them  to  recede  a  certain  distance,  condensing  those 
that  are  before  them  ;  the  impulse  is  finally  overcome  by 
the  resistance  arising  from  this  condensation.  There, 

What  is  meant  by  the  interference  of  waves  ?  When  will  two  systems 
of  waves  not  interfere  ?  When  will  they  interfere  ?  What  is  meant  by 
the  inflexion  of  waves  ?  What  are  the  phenomena  of  vibrations  in  elastic 
media,  as  atmospheric  air  ? 


INTERFERENCE   OF   WAVES.  155 

therefore,  arises  a  sphere  of  air,  the  superficies  or  shell 
of  which  has  a  maximum  density.  Reaction  now  sets  in, 
the  sphere  contracts,  and  the  returning  particles  come  to 
their  original  positions.  But  as  a  disturbance  on  the  sur- 
face of  a  liquid  gives  origin  to  a  progressive  wave,  so  does 
the  same  thing  take  place  in  the  air. 

By  the  intensity  of  vibration  of  a  wave  we  mean  the 
relative  disturbance  of  its  moving  particles,  or  the  mag- 
nitude of  the  excursions  they  make  on  each  side  of  their 
line  of  rest.  Thus,  on  the  surface  of  water  we  may  have 
waves  "  mountains  high,"  or  less  than  an  inch  high  ;  the 
intensity  of  vibration  in  the  former  is  correspondingly 
greater  than  in  the  latter  case. 

In  aerial  waves,  precisely  as  in  the  surface-waves  of 
water,  interference  arises  under  the  proper  conditions. 
Thus,  let  a  m  p  h,  Fig.  178,  be  a  wave  advancing  toward 


c,  arid  let  m  n,  o  p  be  the  intensity  of  its  vibration,  or  the 
maximum  distances  of  the  excursions  of  its  vibrating  par- 
ticles. Then  suppose  a  second  wave,  originating  at  b  (a 
distance  from  a  precisely  equal  to  one  wave  length),  the 
intensity  of  vibration  of  which  is  represented  by  q  r.  The 
motions  of  this  second  wave  coinciding  throughout  its 
length  with  the  motions  of  the  first,  the  force  of  both  sys- 
tems is  increased.  The  intensity,  therefore,  of  the  wave, 
arising  from  their  conjoint  action  at  any  point,  q  will  be 
equal  to  the  sum  of  their  intensities,  q  r,  q  s — that  is,  it 
will  be  q  t,  and  for  any  other  point,  v,  it  will  be  equal  to 
the  sum  of  v  w  and  v  u — that  is,  v  x.  So  the  new  wave 
will  be  represented  by  b  t  g  x  h. 

Now  let  things  remain  as  before,  except  that  the  point 
of  impact  of  the  second  wave,  instead  of  being  one  whole 
wave  from  «,  is  only  half  a  wave,  the  effects  on  any  parti- 

What  is  meant  by  the  intensity  of  vibration  ?  Trace  the  phenomena 
of  interference  represented  in  Figs.  178  and  179  respectively. 


156 


INTERFERENCE   OF    NAVES, 


cle,  such  as  q,  take  place  in  opposite  directions,  the  sec- 
ond wave  moving  it  with  the  intensity  and  direction  q 

fif.  17*. 


r,  the  first  with  q  *  —  the  resultant  of  its  movement  in  in- 
tensity and  direction,  will,  therefore,  be  the  difference  of 
these  quantities  —  that  is,  q  t.  And  the  same  reasoning 
continued  gives,  for  the  wave  resulting  from  this  conjoint 
action,  6  t  g  x  k  c. 

Under  the  circumstances  given  in  Fig.  ITS.  the  systems 
of  waves  increase  each  other's  force  :  under  those  of  £$f. 
179,  they  diminish  it  :  or  if  equal  to  one  another  counter- 
act completely,  and  total  interference  results, 

Waves  in  the  air,  as  they  expand,  have  their  superfi- 
cies continually  increasing,  as  the  squares  of  their  radii 
of  distance  from  the  original  point  of  disturbance.  Hence 
the  effect  of  all  such  waves  is  to  diminish  as  the  squares 
of  the  distances  incress 


-v  c^5  :-e 


ACOUSTICS.  157 


THE   LAWS   OF   SOUND. 

ACOUSTICS. 


LECTURE  XXXIII. 

PRODUCTION  OF  SOUND. —  The  Note  Depends  on  Frequen- 
cy of  Vibration. — Distinguishing  Powers  of  the  Ear. — 
Soniferous  Media. — Origin  of  Sounds  in  the  Air. — Elas- 
ticity Required  and  Given  in  the  Case  of  Strings  by 
Stretching. — Rate  of  Velocity  of  Sounds. — All  Sounds 
Transmitted  with  Equal  Speed. — Distances  Determined 
by  it. — High  and  Low  Sounds. —  Three  Directions  of 
Vibration. — Intensity  of  Sound. — Quality  of  Sounds. — 
TJie  Diatonic  Scale. 

WHEN  a  thin  elastic  plate  is  made  to  vibrate,  one  of  its 
ends  being  held  firm  and  the  other  being  free,  and  its  length 
limited  to  a  few  inches,  it  emits  a  clear  musical  note.  If 
it  be  gradually  lengthened,  it  yields  notes  of  different 
characters,  and  finally  all  sound  ceases,  the  vibrations  be- 
coming so  slow  that  the  eye  can  follow  them  without  dif- 
ficulty. 

This  instructive  experiment  gives  us  a  clear  insight  into 
the  nature  of  musical  sounds,  and,  indeed,  of  all  sounds 
generally.  A  substance  which  is  executing  a  vibratory 
movement,  provided  the  vibrations  follow  one  another 
with  sufficient  rapidity,  yields  a  musical  sound;  but  when 
those  vibrations  fall  below  a  certain  rate,  the  ear  can  no 
longer  distinguish  the  effect  of  their  impulsions. 

The  number  of  vibrations  which  such  a  plate  makes  in 

What  is  the  nature  of  a  musical  sound  ?  Under  what  circumstances 
does  the  sound  become  inaudible  ?  What  regulates  the  number  of  vibra- 
tions of  an  elastic  plate  ? 


158  SOUND    ARISES    IN    VIBRATIONS. 

a  given  time  depends  upon  its  length,  being  inversely  as 
the  square  of  the  length  of  the  vibrating  part.  Thus,  if 
we  take  a  given  plate  and  reduce  its  length,  the  vibra- 
tions will  increase  in  rapidity ;  when  it  is  half  as  long  it 
vibrates  four  times  as  fast;  when  one  fourth,  sixteen 
times,  &c. 

All  sounds  arise  in  vibratory  movements,  and  musical 
notes  differ  from  one  another  in  the  rapidity  of  their  vi- 
brations— the  more  rapidly  recurring  or  frequent  the  vi- 
bration the  higher  the  note. 

There  is,  therefore,  no  difficulty  in  determining  how- 
many  vibrations  are  required  to  produce  any  given  note. 
We  have  merely  to  find  the  length  of  a  plate  which  will 
yield  the  note  in  question,  knowing  previously  what  length 
of  it  is  required  to  make  a  determinate  number  of  vibra- 
tions in  a  given  space  of  time.  Thus  it  has  been  found 
that  the  ear  can  distinguish  a  sound  made  by  15  vibra- 
tions in  a  second,  and  can  still  continue  to  hear  though 
the  number  reaches  48,000  per  second. 

That  all  sounds  arise  in  these  pulsatory  movements 
common  observations  abundantly  prove.  If  we  touch  a 
bell,  or  the  string  of  a  piano,  or  the  prong  of  a  tuning- 
fork,  we  feel  at  once  the  vibratory  action,  and  with  the 
cessation  of  that  motion  the  sound  dies  away. 

.  180.  But  the  pulsations  of  such  a  body 

are  not  alone  sufficient  to  produce  the 
phenomena  of  sound.  Media  must 
intervene  between  them  and  the  or- 
gan of  hearing.  In  most  cases  the 
medium  is  atmospheric  air,  and  when 
this  is  taken  away  the  effect  of  the 
vibrations  wholly  ceases.  Thus,  a 
bell  or  a  musical  snuff-box,  under  an 
exhausted  receiver,  as  in  Fig.  180, 
can  no  longer  be  heard;  but  on  read- 
mitting the  air  the  sound  becomes 
audible.  The  sounding  body,  there- 
fore, requires  a  soniferous  medium  to  propagate  its  im- 
pulses to  the  ear. 

Atmospheric  air  is  far  from  being  the  only  soniferous 

How  may  the  number  of  vibrations  which  constitute  any  sound  be  de- 
termined ?  How  may  it  be  proved  that  all  sounds  arise  in  vibratory  move- 
ments ?  How  may  it  be  proved  that  a  soniferous  medium  is  required  ? 


SONIFEROUS    MEDIA.  159 

medium.  Sounds  pass  with  facility  through  water ;  the 
scratching  of  a  pin  or  the  ticking  of  a  watch  may  be  heard 
by  the  ear  applied  at  the  end  of  a  very  long  plank  of 
wood.  Any  uniform  elastic  medium  is  capable  of  trans- 
mitting sound ;  but  bodies  which  are  imperfectly  elastic, 
or  have  not  an  uniform  density,  impair  its  passage  to  a 
corresponding  degree. 

The  effect  of  a  vibrating  spring,  or,  indeed,  of  any  vi- 
brating body  on  the  atmospheric  air,  is  to  establish  in  it  a 
series  of  condensations  and  rarefactions  which  give  rise 
to  waves.  These,  extending  spherically  from  the  point  of 
disturbance,  advance  forward  until  they  impinge  on  the 
ear,  the  structure  of  which  is  so  arranged  that  the  move- 
ment is  impressed  on  the  auditory  nerves,  and  gives  rise 
to  the  sensation  which  we  term  sound. 

Both  the  sonorous  body  and  the  soniferous  medium 
must,  therefore,  be  elastic,  the  regularity  of  the  pulsa- 
tions of  the  former  depends  upon  the  uniformity  of  its 
elasticity.  In  the  case  of  strings,  we  give  them  the  re- 
quisite degree  of  elastic  force  by  stretching  them  to  the 
proper  degree.  And,  as  the  undulatory  movements  which 
arise  in  the  soniferous  medium  are  not  instantaneous,  but 
successive,  it  follows  that  the  transmission  of  sound  in 
any  medium  requires  time.  That  this  is  the  case,  we 
may  satisfy  ourselves  by  remarking  the  period  that  elapses 
between  seeing  the  flash  of  a  gun  and  hearing  the  report. 
It  is  greater  as  we  are  removed  to  a  greater  distance.  In 
different  media,  the  velocity  of  transmission  depends  on 
the  density  and  specific  elasticity.  It  has  been  found,  by 
experiment,  that  in  tranquil  air  the  velocity  of  sound  at 
60°,  and  at  an  average  state  of  moisture,  is  1120  feet  in 
a  second.  The  wind  accelerates  or  retards  sound,  ac- 
cording to  its  direction,  damp  air  transmits  it  more  slowly 
than  dry,  and  hot  air  more  rapidly  than  cold,  the  velocity 
increasing  about  1*1  foot  for  every  Fahrenheit  degree. 

In  a  soniferous  medium,  all  sounds  move  equally  fast ; 
it  is  wholly  immaterial  what  may  be  their  quality  or  their 


Mention  some  such  soniferous  media.  How  is  it  that  sounds  are  finally 
perceived  by  the  ear  ?  What  condition  is  required  both  for  the  sounding 
body  and  soniferous  medium  ?  How  may  sufficient  elasticity  be  given  in 
the  case  of  strings  ?  Does  the  transmission  of  sound  require  time  ?  What 
is  the  velocity  of  sound  per  second '(  What  is  the  effect  of  the  wind,  damp- 
ness, or  change  of  temperature  ? 


160  VELOCITY    OF    SOUND. 

intensity.  Thus,  we  know  that  even  the  most  intricate 
music  executed  at  a  distance  is  heard  without  any  discord, 
arid  precisely  as  it  would  be  close  at  hand.  Nor  does  it 
matter  whether  it  be  by  the  human  voice,  a  flute,  a.bugle, 
or,  indeed,  by  many  different  instruments  at  once,  the 
relation  of  the  difference  of  sounds  is  accurately  preserv- 
ed. But  this  can  only  take  place  as  a  consequence  of  the 
equal  velocity  of  transmission  ;  for  if  some  of  these  sounds 
moved  faster  than  others  discord  must  inevitably  ensue. 

The  experiments  of  Colladon  and  Sturm  on  the  Lake 
of  Geneva  show  that  the  velocity  in  water  is  about  four 
times  that  in  air,  being  4708  feet  in  a  second.  With  re- 
spect to  solid  substances,  it  is  stated  that  the  velocity  in 
air  being  1,  that  in  tin  is  7s,  in  copper  12,  in  glass  17. 

Advantage  is  sometimes  taken  of  these  principles  to 
determine  distances.  If  we  observe  the  time  elapsing 
between  the  flash  of  a  gun  and  hearing  the  sound,  or  be- 
tween seeing  lightning  and  hearing  the  thunder,  every 
second  answers  to  1120  feet. 

Sounds  are  of  different  kinds  :  some  are  low  or  high, 
grave  or  acute,  according  as  the  vibrations  are  slower  or 
faster.  Again :  the  intensity  of  vibration  or  the  magni- 
tudes of  the  excursions  which  the  vibrating  particles 
make  determine  the  force  of  sounds,  an  intense  vibra- 
tion giving  a  loud,  and  a  less  vibration  a  feeble  sound. 

The  vibrations  of  a  soniferous  body  may  take  place  in 
three  directions  :  they  may  be  longitudinal,  transverse, 
or  rotatory  vibrations ;  or,  indeed,  they  may  all  co-exist. 
Fie- J81-  A  body  may  be  divided  into  vibrat- 

ing parts,  separated  from  one  another 
by  nodal  points  or  lines.  Thus,  if  we 
take  a  glass  or  metal  plate,  and  having 
strewed  its  surface  with  fine  dry  sand, 
and  holding  it  firmly  at  one  point  between  the  thumb 
arid  finger,  or  in  a  clamp,  as  represented  in  Fig.  181, 
draw  a  violin  bow  across  its  edge,  it  yields  a  musical 
note,  and  the  sand  is  thrown  off  those  places  which  are 
in  motion,  and  collects  on  the  nodal  points,  which  are 
at  rest. 

The  quantity,  or  strength,  or  intensity  of  a.  sound  de 

What  is  the  velocity  of  sounds  in  water  1  Into  what  varieties  may 
sound  be  divided  ?  In  what  directions  may  a  sounding  body  vibrate  I 
How  may  nodal  lines  on  surfaces  be  traced  ? 


NATURE    OF    SOUNDS.  161 

pends  on  the  intensity  of  the  vibrations  and  the  mass  of 
the  sounding  body.  It  also  varies  with  the  distance,  be- 
ing inversely  proportional  to  its  square. 

Musical  sounds  are  spoken  of  as  notes,  or  as  high  and 
low.  Of  two  notes,  the  higher  is  that  which  arises  from 
more  rapid,  and  the  lower  from  slower  vibrations. 

Besides  this,  sounds  differ  in  their  quality.  The  same 
note  emitted  by  a  flute,  a  violin,  a  piano,  or  the  human 
voice  is  wholly  different,  and  in  each  instance  peculiar. 
In  what  this  peculiarity  consists  we  are  not  able  to  say. 

The  several  notes  are  distinguished  by  letters  and 
names ;  we  shall  also  see  presently  that  they  may  be  dis- 
tinguished by  numbers.  They  are — 

C    D    E    F    G    A    B    C. 

Or,  ut,  re,  ini,  fa,  sol,  la,  si,  ut. 

Such  a  series  of  sounds  passes  under  the  name  of  the 
diatonic  scale. 


LECTURE  XXXIV. 

PHENOMENA  OP  SOUND. — Notes  in  Unison. — Octave. — In- 
terval of  Sounds. —  Melody. —  Harmony. —  The  Mono- 
chord. — Length  of  Cord  and  Number  of  Vibrations  re- 
quired for  each  Note. — Laws  of  Vibrations  in  Cords, 
Rods,  Planes. — Acoustic  Figures  on  Plates. —  Vibration 
of  Columns  of  Air. — Interference  of  Sounds. —  Whisper- 
ing Galleries. — Echoes. — Speaking  and  Hearing-  Trum- 
pet. 

Two  notes  are  said  to  be  in  unison  when  the  vibrations 
which  cause  them  are  performed  in  equal  times.  If  the 
one  makes  twice  as  many  vibrations  as  the  other,  it  is 
said  to  be  its  octave,  and  the  relation  or  interval  there  is 
between  two  sounds  is  the  proportion  between  their  re- 
spective numbers  of  vibrations. 

There  are  combinations  of  sounds  which  impress  our 
organs  of  sense  in  an  agreeable  manner,  and  others  which 

On  what  does  the  intensity  of  sound  depend  ?  What  is  it  that  determines 
the  highness  or  lowness  of  notes  ?  What  is  meant  by  the  quality  of  sounds  ? 
How  may  notes  be  distinguished  ?  When  are  notes  in  unison  ?  What  is 
an  octave  ?  What  is  the  relation  or  interval  of  sounds  ? 


162 


THE    MONOCHORD. 


produce  a  disagreeable  effect.  In  this  sense,  we  speak 
of  the  former  as  being  in  unison,  and  the  latter  as  being 
discordant.  A  combination  of  harmonious  sounds  is  a 
chord,  a  succession  of  harmonious  notes  a  melody,  and  a 
succession  of  chords  harmony. 

We  have  remarked  in  the  last  lecture  that  sounds  may 
be  expressed  by  numbers  as  well  as  by  letters  or  names, 
and  their  relations  to  one  another  clearly  exhibited.  For 
this  purpose,  we  may  take  the  monochord  or  sonometer, 
C  C',  Fig.  182,  an  instrument  consisting  of  a  wire  or 

Fig.  182. 


"n 

TO 

JCF             ®                           H 

IT             F 

0 

M       ill 

03 

catgut  stretched  over  two  bridges,  F  F',  which  are  fast- 
ened on  a  basis,  S  S' ;  one  end  of  the  cord  passes  over  a 
pulley,  M,  and  may  be  strained  to  any  required  degree 
of  weights,  P.  The  length  of  the  string  vibrating  may 
be  changed  by  pressing  it  with  the  finger  upon  a  movable 
piece,  H,  which  carries  an  edge,  T,  and  the  case  beneath 
is  divided  into  parts  which  exhibit  the  length  of  the  vi- 
brating part  of  the  wire.  The  upper  part  of  Fig.  182 
shows  a  horizontal  view  of  the  monochord,  the  lower  a 
lateral  view.  The  instrument  here  represented  has  two 
strings,  one  of  catgut  and  one  of  wire. 

Now,  it  is  to  be  understood  that  the  number  of  vibra- 
tions of  such  a  cord  are  inversely  as  its  length  ;  that  is, 
if  the  whole  cord  makes  a  given  number  of  vibrations  in 
one  second,  when  you  reduce  its  length  to  one  half  it  will 
make  twice  as  many ;  if  to  one  third,  thrice  as  many,  &c. 

What  is  a  chord,  a  melody,  and  harmony,  ?    Describe  the  monochord. 


VIBRATIONS    OF    CORDS.  163 

Suppose  the  cord  is  stretched  so  as  to  give  a  clear  sound, 
which  we  may  designate  as  C,  and  the  movable  bridge 
is  then  advanced  so  as  to  obtain  successively  the  other 
notes  of  the  gamut,  D,  E,  F,  G,  A,  B,  C,  it  will  be  found 
that  these  are  given  when  the  lengths  of  the  cord,  com- 
pared with  its  original  length,  are — 

Name  of  note          .        .        .        CDEFGABC 
Length  of  cord       .        .        .         1,  f,  j,   f,    §,  f,  T85,  ±. 

but  as  the  number  of  vibrations  is  in  the  inverse  ratio  of 
the  lengths  of  the  vibrating  cords,  we  shall  have  for  the 
number  of  vibrations,  if  we  represent  by  1,  the  number 
that  gives  C,  the  following  for  the  other  notes  : 

Name  of  note          .        .        .        CDEFGABC 
Number  of  vibrations     .  1,   |,  |,  f,   |,  |,  y  2. 

From  C  to  C  is  an  octave,  and  from  this  we  gather  that, 
in  the  octave,  the  higher  note  makes  twice  as  many  vibra- 
tions as  the  fundamental  note,  and  that  between  these 
there  are  other  intervals,  which,  heard  in  succession,  are 
harmonious  ;  the  eight,  therefore,  constitute  a  scale,  com- 
monly called  the  diatonic  scale. 

Musical  instruments  are  of  different  kinds,  depending 
on  the  vibrations  of  cords,  rods,  planes,  or  columns  of  air. 

It  has  already  been  stated,  that  the  number  of  vibra- 
tions of  a  cord  is  inversely  as  its  length — the  number  also 
increases  as  the  square  root  of  the  force  that  stretches  it ; 
thus,  the  octave  is  given  by  the  same  string  when  stretch- 
ed four  times  as  strongly  ;  the  material  of  the  string, 
whether  it  be  catgut,  iron,  &c.,  also  affects  the  note. 

In  rods  the  height  of  the  note  is  directly  as  the  thick- 
ness, and  inversely  as  the  square  of  the  length.  The 
quality  of  the  material  also,  in  respect  of  elasticity,  deter- 
mines the  note. 

The  foregoing  observations  apply  to  transverse  vibra- 
tions of  cords  and  rods ;  but  they  may  be  also  made  to 
execute  longitudinal  and  torsion  vibrations,  the  conditions 
of  which  are  different. 

In  planes  held  by  one  point,  and  a  bow  drawn  across 
at  another,  or  struck  by  a  blow,  sounds  are  emitted,  and 
by  the  aid  of  sand  nodal  lines  may  be  traced.  Thus,  in 
Fig.  183,  a  is  the  point,  in  each  instance,  at  which  the 

What  lengths  of  a  cord  are  required  to  give  the  notes  of  the  gamut  ?  What 
are  the  corresponding  number  of  vibrations?  What  is  the  diatonic  scale? 
What  are  the  laws  for  the  vibration  of  cords  ?  What  in  the  case  of  rods  ? 


164 


ACOUSTIC    FIGURES. 


plate  is  held,  and  b  that  at  which  the  bow  is  applied ;  the 
sand  arranges  itself  in  the  dotted  lines. 

The  two  large  figures  are  formed  by  putting  together 
four  smaller  plates,  in  one  instance  bearing  the  nodal 
lines,  represented  at  I,  and,  in  the  other,  at  II.  They 
may,  however,  be  directly  generated  on  one"  large  plate 
of  glass  by  holding  it  at  a,  touching  it  at  w,  and  drawing 
the  bow  across  it  at  b. 


Circular  plates,  a  in  III,  may  be  made  to  bear  a  four- 
rayed  star,  by  holding  them  in  the  center,  drawing  the 
bow  at  any  point  at  b,  and  touching  the  plate  at  a  point 
45°  distant  from  the  bow  ;  but  if  the  plate  be  touched  30°, 
60°,  or  90°  off,  it  produces  a  six-rayed  star,  Fig.  IV. 

Columns  of  air  may  be  made  to  emit  sounds  by  being 
thrown  into  oscillation,  as  in  horns,  flutes,  clarionets,  &c. 
In  these  the  column  of  air,  included  in  the  tube  of  the  in- 
strument, is  made  to  vibrate  longitudinally.  The  height 
of  the  note  is  inversely  proportional  to  the  length  of  the 
column,  and  therefore  different  notes  may  be  obtained 
by  having  apertures,  at  suitable  distances,  in  the  side  of 
the  tube,  as  in  the  flute. 

Two  sounds  may  be  so  combined  together  that  they  shall 

In  the  case  of  planes  how  may  the  nodal  lines  be  varied  ?  How  may 
columns  of  air  be  made  to  vibrate?  How  is  the  length  of  the  vibrating 
column  varied  in  different  wind  instruments  ? 


INTERFERENCE    OF    SOUNDS.  165 

mutually  destroy  each  other's  effect,  and  silence  result. 
This  arises  from  interference  taking  place  in  the  aerial 
waves,  the  laws  of  which  are  those  given  in  Lecture  XXXII. 
The  following  instances  will  illustrate  these  facts. 

When  a  tuning-fork  is  made  to  vibrate,  and  is  turned 
round  upon  its  axis  near  the  ear,  four  periods  may  be  dis- 
covered during  every  revolution  in  which  the  sound  in- 
creases or  declines.  .4  - 

If  we  take  two  tuning-forks  of  the  same  note,  a  dt 
Fig.  184,  and  fasten  a  circle  of  cardboard,  Fig.  184. 
half  an  inch  in  diameter,  on  one  of  the  prongs 
of  each,  and  make  one  of  the  forks  a  little 
heavier  than  the  other,  by  putting  on  it  a  drop 
of  wax,  and  then  filling  a  jar,  b,  to  such  a 
height  with  water,  that  either  of  the  forks, 
when  held  over  it,  will  make  it  resound,  so 
long  as  only  one  is  held,  there  will  be  a  con- 
tinuous note,  without  pause  or  interruption  ; 
but  if  both  are  held  together,  there  will  be  periods  of 
silence  and  periods  of  sound,  according  as  the  longer 
waves,  arising  from  one  of  the  forks,  overtakes  and  inter- 
feres with  the  shorter  waves,  arising  from  the  other. 

Sounds  undergo  reflexion,  and  may  therefore  be  directed 
by  surfaces  of  suitable  figure.  If,  in  the  focus  of  a  concave 
mirror  a  watch  be  placed,  its  ticking  may  be  heard  at  a 
great  distance  in  the  focus  of  a  second  mirror,  placed  so 
as  to  receive  the  sound-waves  of  the  first. 

On  similar  principles  also  whispering-galleries  depend. 
These  are  so  constructed  that  a  low  whisper  uttered  at 
one  point  is  reflected  to  a  focus  at  another,  in  which  it 
may  be  distinctly  heard,  while  it  is  inaudible  in  other  po- 
sitions. The  dome  of  St.  Paul's  cathedral,  in  London,  is 
an  example. 

Echoes  are  reflected  sounds.  Thus,  if  a  person  stands 
in  front  of  a  vertical  wall,  and  at  a  distance  from  it  of 
about  62  £  feet,  if  he  utters  a  syllable,  he  will  hear  a  sound 
which  is  the  echo  of  it.  If  there  be  a  series  of  such  ver- 
tical obstacles,  at  suitable  distances,  the  same  sound  may 
be  repeated  many  successive  times.  A  good  ear  can  dis- 
tinguish nine  distinct  sounds  in  a  second  ;  and,  as  a  sound 

Give  some  illustrations  of  the  interference  of  sound.    How  may  it  be 
proved  that  sounds  undergo  reflexion  ?    What  are  whispering-galleries  '. 
Under  what  circumstances  do  echoes  arise  ? 


166 


ECHOES. 


travels  1120  feet  in  the  same  time,  for  the  echo  to  be 
clearly  distinguished  from  its  original  sound,  it  must  travel 
125  feet  in  passing  to  and  from  the  reflecting  surface,  that 
is,  the  reflector  must  be  at  least  62£  feet  distant. 

Remarkable  echoes  exist  in  several  places.  One  near 
Milan  repeats  a  sound  thirty  times.  The  ancients  men- 
tion one  which  could  repeat  the  first  verse  of  the 

Fig,  185. 


eight  times.  On  the  banks  of  rivers — as,  for  example,  on 
the  Rhine,  as  represented  in  Fig.  185 — sounds  are  often 
echoed  from  the  rocks,  rebounding,  as  at  1,  2,  3,  4,  from 
side  to  side. 

Speaking-trumpets  depend  on  the  reflection  of  sound. 
Fig.  186.  The  divergence 

is  prevented  by 
the  sides  of  its 
tube  ;  and  if  the 
instrument  is  of 
a  suitable  figure, 
the  rays  of sound 
issue  from  it,  as 
seen  in  Fig.  186,  in  a  parallel  direction.  Its  efficiency 
depends  on  its  length.  It  is  stated  that  through  such  an 
instrument,  from  18  to  24  feet  long,  a  man's  voice  can  be 
heard  at  a  distance  of  three  miles.  Under  common  cir- 
cumstances, the  greatest  distances  at  which  sounds  have 

Why  must  two  reflecting  surfaces  be  at  a  certain  distance  ?  What  is  the 
construction  of  the  speaking-trumpet  ? 


HEARING-TRUMPETS  107 

been  heard  are  usually  estimated  as  follows :  the  report 
of  a  musket,  8000  paces;  the  march  of  a  company  of  sol- 
diers at  night,  830  paces;  a  squadron  galloping,  1080  ;  the 
voice  of  a  strong  man,  in  the  open  air,  230.  But  the  ex- 
plosions of  the  volcano  of  St.  Vincent  were  heard  at 
Demerara,  345  miles;  and,  at  the  siege  of  Antwerp,  the 
cannonading  was  heard,  in  the  mines  of  Fig.  187. 
Saxony,  370  miles. 

The  hearing-trumpet  is  for  the  purpose 
of  collecting  rays  of  sound  by  reflexion, 
and  transmitting  them  to  the  ear.  Its 
mode  of  action  is  represented  at  Fig.  187. 

At  what  distance  can  sounds  be  heard?    What  is  the  construction  of 
the  hearing-trumpet. 


168  OPTICS. 


PROPERTIES    OF    LIGHT. 

OPTICS. 


LECTURE  XXXV. 

PROPERTIES  OF  LIGHT. —  Theories  of  the  Nature  of  Light. 
— Sources  of  Light. — Phosphorescence. —  Temperature  of 
a  red  Heat. — Effects  of  Bodies  on  Light. — Passage  in 
straight  Lines. — Production  of  Shadows. —  Umbra  and 
Penumbra. 

HAVING  successively  treated  of  the  general  mechanical 
properties  of  gases,  liquids,  solids,  and  the  laws  of  motion, 
we  are  led,  in  the  next  place,  to  the  consideration  of  cer- 
tain agents  or  forces — light,  heat,  electricity.  These,  by 
many  philosophers,  are  believed  to  be  matter,  in  an  im- 
ponderable state  ;  they  are  therefore  spoken  of  as  im- 
ponderable substances.  By  others  their  effects  are  re- 
garded as  arising  from  motions  or  modifications  impressed 
on  a  medium  everywhere  present,  which  passes  under 
the  name  of  THE  ETHER. 

Applying  these  views  to  the  case  of  light,  two  different 
hypotheses,  respecting  its  constitution,  obtain.  The  first, 
which  has  the  designation  of  the  theory  of  emission,  re- 
gards light  as  consisting  of  particles  of  amazing  minute- 
ness, which  are  projected  by  the  shining  body,  in  all  di- 
rections, and  in  straight  lines.  These  impinging  eventu- 
ally on  the  organ  of  vision,  give  rise  to  the  sensation 
which  we  speak  of  as  brightness  or  light.  To  the  other 
theory,  the  title  of  undulatory  theory  is  given  ;  it  supposes 
that  there  exists  throughout  the  universe  an  ethereal  me- 
dium, in  which  vibratory  movements  can  arise  somewhat 
analogous  to  the  movements  which  give  birth  to  sounds 

Name  the  imponderable  substances.  What  other  theory  is  there  re- 
specting their  nature  ?  What  is  the  theory  of  emission  ?  What  is  the 
foundation  of  the  undulatory  theory  ? 


SOURCES    OF.  LIGHT.  169 

in  the  air;  and  these  passing  through  the  transparent 
parts  of  the  eye,  and  falling  on  the  retina,  affect  it  with 
their  pulsations,  as  waves  in  the  air  affect  the  auditory 
nerve,  but  in  this  case  give  rise  to  the  sensation  of  light, 
as  in  the  other  to  sound. 

There  are  many  different  sources  of  light — some  are 
astronomical  and  some  terrestrial.  Among  the  former 
may  be  mentioned  the  sun  and  the  stars — among  the  lat- 
ter, the  burning  of  bodies,  or  combustion,  to  which  we 
chiefly  resort  for  our  artificial  lights,  as  lamps,  candles,  gas 
flames.  Many  bodies  are  phosphorescent,  that  is  to  say, 
emit  light  after  they  have  been  exposed  to  the  sun  or  any 
shining  source.  Thus,  oyster-shells,  which  have  been  cal- 
cined with  sulphur,  shine  in  a  dark  place  after  they  have 
been  exposed  to  the  light,  and  certain  diamonds  do  the 
same.  So,  too,  during  processes  of  putrefaction,  or  slow 
decay,  light  is  very  often  emitted,  as  when  wood  is  mould- 
ering or  meat  is  becoming  putrescent.  The  source  of 
the  luminousness,  in  these  cases,  seems  to  be  the  same  as 
in  ordinary  combustions,  that  is,  the  burning  away  of  car- 
bon and  hydrogen  under  the  influence  of  atmospheric  air; 
but,  in  certain  cases,  the  functions  of  life  give  rise  to  an 
abundant  emission  of  light,  as  in  fireflies  and  glowworms ; 
these  continue  to  shine  even  under  the  surface  of  water, 
and  there  is  reason  to  believe  that  the  phenomenon  is  to  a 
considerable  extent  subject  to  the  volition  of  the  animal. 
All  solid  substances,  when  they  are  exposed  to  a  cer- 
tain degree  of  heat,  become  incandescent  or  emit  light. 
When  first  visible  in  a  dark  place,  this  light  is  of  a  red- 
dish color,  but  as  the  temperature  is  carried  higher  and 
higher  it  becomes  more  brilliant,  being  next  of  a  yellow, 
and  lastly  of  a  dazzling  whiteness.  For  this  reason  we 
sometimes  indicate  the  temperature  of  such  bodies,  in  a 
rough  way,  by  reference  to  the  color  they  emit :  thus  we 
speak  of  a  red  heat,  a  yellow  heat,  a  white  heat.  I  have 
recently  proved  that  all  solid  substances  begin  to  emit 
light  at  the  same  degree  of  heat,  and  that  this  answers  to 
977°  of  Fahrenheit's  thermometer  ;  moreover,  as  the  tern- 
Mention  some  of  the  sources  of  light.  What  is  meant  by  phospho- 
rescence ?  To  what  source  may  the  light  emitted  during  putrefaction  and 
decay  be  attributed  ?  What  is  there  remarkable  in  the  shining  of  glow- 
worms and  fireflies  1  What  is  meant  by  incandescence  ?  What  succes- 
sion of  colors  is  perceived  in  self-luminous  bodies  ?  At  what  temperature 
do  all  solids  begin  to  shine  ? 

H 


170  PATH^  OF    RAYS. 

perature  rises  the  brilliancy  of  the  light  rapidly  increases, 
so  that  at  a  temperature  of  2600°  it  is  almost  forty  times  as 
intense  as  at  1900°.  At  these  high  temperatures  an  ele- 
vation of  a  few  degrees  makes  a  prodigious  difference  in 
the  brilliancy.  Gases  require  to  be  brought  to  a  far  higher 
temperature  than  solids  before  they  begin  to  emit  light. 

Non-luminous  bodies  become  visible  by  reflecting  the 
light  which  falls  on  them.  In  their  general  relations  such 
bodies  may  be  spoken  of  as  transparent  and  opaque.  By 
the  former  we  mean  those  which,  like  glass,  afford  a  more 
or  less  ready  passage  to  the  light  through  them;  by  the 
latter,  such  as  refuse  it  a  passage.  But  transparency  and 
opacity  are  never  absolute — they  are  only  relative.  The 
purest  glass  extinguishes  a  certain  amount  of  the  rays 
which  fall  on  it,  and  the  metals  which  are  commonly 
looked  upon  as  being  perfectly  opaque  allow  light  to  pass 
through  them,  provided  they  are  thin  enough.  Thus  gold 
leaf  spread  upon  glass  transmits  a  greenish-colored  light. 

The  rays  of  light,  from  whatever  source  they  may  come, 
move  forward  in  straight  lines,  continuing  their  course 
until  they  are  diverted  from  it  by  the  interposition  of 
some  obstacle,  or  the  agency  of  some  force.  That  this 
rectilinear  path  is  followed  maybe  proved  by  a  variety  of 
facts.  Thus,  if  we  intervene  an  opaque  body  between 
any  object  and  the  eye,  the  moment  the  edge  of  that  body 
comes  to  the  line  which  connects  the  object  and  the  «ye 
the  object  is  cut  off  from  our  view.  In  a  room  into  which 
a  sunbeam  is  admitted  through  a  crevice,  the  path  which 
the  light  takes,  as  is  marked  out  by  the  motes  that  float  in 
the  air,  is  a  straight  line. 

By  a  ray  of  light  we  mean  a  straight  line  drawn  from 
the  luminous  body,  marking  out  the  path  along  which  the 
shining  particles  pass. 

A  shining  body  is  said  to  radiate  its  light,  because  it 
projects  its  luminous  particles  in  straight  lines,  like  radii, 
in  every  direction,  and  these  falling  on  opaque  bodies 
and  being  intercepted  by  them,  give  rise  to  the  produc- 
tion of  shadows. 


At  what  rate  does  the  light  increase  as  the  temperature  rises?  Are 
solids  or  gases  most  readily  made  incandescent?  How  dp  non-luminous 
bodies  become  visible  ?  What  classes  are  they  divided  into  ?  Are  trans- 
parency and  opacity  absolute  qualities  ?  Prove  that  rays  move  in  straight 
lines.  What  is  meant  by  radiation  ?  How  are  shadows  produced  ? 


SHADOWS. 


171 


If  the  light  is  emitted  by  a  single  luminous  point,  the 
boundary  of  the  shadow  can  be  obtained  by  drawing 
straight  lines  from  the  lumi-  Fig.  iss. 

nous  point  to  every  point  on 
the  edge  of  the  body,  and  pro- 
ducing them.  Thus,  let  a,  Fig. 
188,  be  the  luminous  point,  If 
c  the  opaque  body ;  by  draw- 
ing the  lines  ab,ac,  and  pro- 
ducing them  to  d  and  e  the 
boundary  and  figure  of  the 
shadow  may  be  exhibited. 

But  if  the  luminous  body, 
as  in  most  instances  is  the 
case,  possesses  a  sensible 
magnitude ;  if  it  is,  for  example,  the  sun  or  a  flame,  an 
opaque  body  will  cast  two  shadows,  which  pass  respect- 
ively under  the  names  of  the  umbra  and  penumbra — the 
former  being  dark  and  the  latter  partially  illuminated. 
This  may  be  illustrated  by  Fig.  189,  in  Fig.  189 

which  a  b  is  the  flame  of  a  candle  or 
any  other  luminous  source,  having  a 
sensible  magnitude,  c  d  the  opaque 
body.  Now  the  straight  lines,  a  c  f, 
a  d  k,  drawn  from  the  top  of  the  flame 
to  the  edges  of  the  opaque  body  and 
produced,  give  the  shadow  for  that 
point  of  the  flame ;  and  the  lines  bee, 
b  d  g,  drawn  in  like  manner  from  the 
bottom  of  the  flame,  give  the  shadow  for  that  point.  But 
we  see  that  the  space  between  g  and  k,  which  belongs  to 
the  shadow  for  the  top  of  the  flame,  is  not  perfectly  dark, 
because  it  is  so  situated  as  to  be  partially  illuminated  by 
the  bottom  of  the  flame — and  a  similar  remark -may  be 
made  as  respects  the  space,  f  e,  which  receives  light  from 
the  top  of  the  flame.  But  the  remaining  space,  f  g,  re- 
ceives no  light  whatever — it  is  totally  dark — and  we  there- 
fore call  it  the  umbra,  while  the  partially-illuminated  re- 
gions, fe  and  g  h,  are  the  penumbra. 

Trace  the  shadow  of  a  body  formed  by  a  luminous  point.  Trace  the 
formation  of  a  shadow  when  the  luminous  source  is  of  sensible  size.  What 
is  the  umbra  ?  What  is  the  penumbra  ? 


172  PHOTOMETRY. 


LECTURE  XXXVI. 

OF  THE  MEASURES  OF  THE  INTENSITY  AND  VELOCITY  OF 
LIGHT. — Conditions  oftlie  Intensity  of  Light. —  Of  Pho- 
tometric Methods. — Rumford's  Method  by  Shadows. — 
Ritchie's  Photometer. — Difficulties  in  Colored  Lights. — 
Masson's  Method. —  Velocity  of  Light  Determined  by  the 
Eclipses  of  Jupiter's  Satellites. —  The  same  by  the  Aber- 
ration of  the  Fixed  Stars. 

BY  Photometry  we  mean  the  measurement  of  the  brill- 
iancy of  light — an  operation  which  can  be  conducted  in 
many  different  ways. 

It  is  to  be  understood  that  the  illuminating  power  of  a 
shining  body  depends  on  several  circumstances :  First, 
upon  its  distance — for  near  at  hand  the  effect  is  much 
greater  than  far  off — the  law  for  the  intensity  of  light  in 
this  respect  being  that  the  brilliancy  of  the  light  is  inversely 
as  the  square  of  the  distance.  A  candle  two  feet  off  gives 
only  one  fourth  of  the  light  that  it  does  at  one  foot,  at  three 
feet  it  gives  only  one  ninth,  &c.  Secondly,  it  depends  on 
the  absolute  intensity  of  the  luminous  surface  :  thus  we 
have  seen  that  a  solid  at  different  degrees  of  heat  emits 
very  different  amounts  of  light,  and  in  the  same  way  the 
flame  of  burning  hydrogen  is  almost  invisible,  and  that 
of  spirits  of  wine  is  very  dull  when  compared  with 
an  ordinary  lamp.  Thirdly,  it  depends  on  the  area  or 
surface  the  shining  body  exposes,  the  brightness  being 
greater  according  as  that  surface  is  greater.  Fourthly, 
in  the  absorption  which  the  light  suffers  in  passing  the 
medium  through  which  it  has  to  traverse — for  even  the 
most  transparent  obstructs  it  to  a  certain  extent.  And 
lastly,  on  the  angle  at  which  the  rays  strike  the  surface 
they  illuminate,  being  most  effective  when  they  fall  per- 
pendicularly, and  less  in  proportion  as  their  obliquity  in- 
creases. 

What  is  photometry  ?  Mention  some  of  the  conditions  which  determine 
the  brilliancy  of  light.  What  is  the  law  of  its  decrease  by  distance?  What 
has  obliquity  of  surfaces  to  do  with  the  result  ? 


173  INTENSITY    OF    LIGHT. 

The  first  and  last  of  the  conditions  here  mentioned,  as 
controlling  the  intensity  of  light — the  effect  of  distance 
and  of  obliquity — may  be  illustrated  as  follows  : — 

Fig.  190. 


1st.  That  the  intensity  of  light  is  inversely  as  the  squares 
of  the  distance.  Let  B,  Fig.  190,  be  an  aperture  in  a 
piece  of  paper,  through  which  rays  coming  from  a  small 
illuminated  point,  A,  pass ;  let  these  rays  be  received  on 
a  second  piece  of  paper,  C,  placed  twice  as  far  from  A  as 
is  B,  it  will  be  found  that  they  illuminate  a  surface  which 
is  twice  as  long  and  twice  as  broad  as  A,  and  therefore 
contains  four  times  the  area.  If  the  paper  be  placed  atD, 
three  times  as  far  from  A  as  is  B,  the  illuminated  space 
will  be  three  times  as  long  and  three  times  as  broad  as  A, 
and  contain  nine  times  the  surface.  If  it  be  at  E,  which 
is  four  times  the  distance,  the  surface  will  be  sixteen  times 
as  great.  All  this  arises  from  the  rectilinear  paths  which 
the  diverging  rays  take,  and  therefore  a  surface  illumina- 
ted by  a  given  light  will  receive,  at  distances  represented 
by  the  numbers  1,  2,  3,  4,  &c.,  quantities  of  light  repre- 
sented by  the  numbers  1,  |,  £,  T'g-,  &c.,  which  latter  are 
the  inverse  squares  of  the  former  numbers. 

2d.  That  the  intensity  of  light  is  dependent  on  the  an- 
gle at  which  the  rays  strike  the  receiving  surface,  being 
most  effective  when  they  fall  perpendicularly,  and  less  in 
proportion  as  the  obliquity  increases.  Let  there  be  two 
surfaces,  D  C  and  E  C,  Fig.  191,  on  which  a  beam  of 
light,  A  B,  falls  on  the  former  perpendicularly  and  on  the 
latter  obliquely — the  latter  surface,  in  proportion  to  its 
obliquity,  must  have  a  larger  area  to  receive  all  the  rays 
which  fall  on  D  C.  A  given  quantity  of  light,  therefore, 

Give  illustrations  of  the  effect  of  distance  and  of  obliquity. 


174  RUMFORD'S  PHOTOMETER. 

Fig.  191. 


is  diffused  over  a  greater  surface  when  it  is  received  ob- 
liquely, and  its  effect  is  correspondingly  less. 

To  compare  different  lights  with  one  another,  Count 
Rumford.  invented  a  process  which  goes  under  the  name 
of  the  method  of  shadows.  The  principle  is  very  simple. 
Of  two  lights,  that  which  is  the  most  brilliant  willcast  the 
deepest  shadow,  and  with  any -light  the  shadow  which  is 
cast  becomes  less  dark  as  the  light  is  more  distant.  If, 
therefore,  we  wish  to  examine  experimentally  the  brill- 
iancy of  two  lights  on  Rumford's  method,  we  take  a 
screen  of  white  paper  and  setting  in  front  of  it  an  opaque 
rod,  we  place  the  lights  in  such  a  position  that  the  two 
shadows  arising  shall  be  close  .together,  side  by  side. 
Now  the  eye  can,  without  any  difficulty,  determine  which 
of  the  two  is  darkest ;  and  by  removing  the  light  which 
has  cast  it  to  a  greater  distance,  we  can,  by  a  few  trials, 
bring  the  two.  shadows  to  precisely  the  same  degree  of 
depth.  It  remains  then  to  measure  the  distances  of  the 
two  lights  from  the  screen,  and  the  illuminating  powers 
are  as  the  squares  of  those  distances. 

Ritchie's  photometer  is  an  instrument  for  obtaining  the 
same  result,  not,  however,  by  the  contrast  of  shadows, 
but  by  the  equal  illumination  of  surfaces.  It  consists  of 
a  box,  a  Z>,  Fig.  192,  six  or.  eight  inches  long  and  one 
broad  and  deep,  in  the  middle  of  which  a  wedge  of  wood, 
feg,  with  its  angle,  e,  upward,  is  placed.  This  wedge 
is  covered  over  with  clean  white  paper,  neatly  doubled  to 
a  sharp  line  at  e.  In  the  top  of  the  box  there  is  a  conical 
tube,  with  an  aperture,  d,  at  its  upper  end,  to  which  the 

What  is  the  principle  of  Rumford's  photometric  process?  How  is  it 
applied  -in  practice  ?  What  is  the  illuminating  power  of  the  lights  propor- 
tional to  ?  Describe  Ritchie's  photometer. 


RITCHIE  3    PHOTOMETEE. 


175 


eye  is  applied,  and  the  whole  may  be  raised  to  any  suitable 
height  by  means  of 
the  stand  c.  On  look- 
ing down  through 
d,  having  previous- 
ly placed  the  two 
lights,  m  n,  the  in- 
tensity of  which  we 
desire  to  determine, 
on  opposite  sides  of  in 
the  box,  they  illu- 
minate the  paper 
surfaces  exposed  to 
them,  e  f  to  jn  and  e  g  to  n,  and  the  eye,  at  d,  sees  both 
those  surfaces  at  once.  By  changing  the  position  of  the 
lights,  we  eventually  make  them  illuminate  the  surfaces 
equally,  and  then  measuring  their  distances  from  ey  their 
illuminating  powers  are  as  the  squares  of  those  dis- 
tances. 

It  is  not  possible  to  apply  either  of  these  methods  in  a 
satisfactory  manner  where,  as  is  unfortunately  often  the 
case,  the  lights  to  be  examined  differ  in  color.  The  eye 
can  form  no  judgment  whatever  of  the  relation  of  bright- 
ness of  two  surfaces  when  they  are  of  different  colors  ; 
and  a  very  slight  amount  of  tint  completely  destroys  the 
accuracy  of  these  processes.  To  some  extent,  in  Ritchie's 
instrument,  this  may  be  avoided,  by  placing  a  colored 
glass  at  the  aperture,  d. 

A  third  photometric  method  has  recently  been  intro- 
duced ;  it  has  great  advantages  over  either  of  the  fore- 
going ;  and  difference  of  color,  which  in  them  is  so  se- 
rious an  obstacle,  serves  in  it  actually  to  increase  the  ac- 
curacy of  the  result.  The  principle  on  which  it  is  found- 
ed is  as  follows :  If  we  take  two  lights,  and  cause  one  of 
them  to  throw  the  shadow  of  an  opaque  body  upon  a 
white  screen,  there  is  a  certain  distance  to  which,  if  we 
bring  the  second  light,  its  rays,  illuminating  the  screen, 
will  totally  obliterate  all  traces  of  the  shadow.  This  dis- 
appearance of  the  shadow  can  be  judged  of  with  great 

What  difficulties  arise  when  the  lights  and  the  shadows  they  give  are 
colored  ?  How  may  these  be  avoided  ?  Describe  another  process  which 
is  free  from  the  foregoing  difficulties.  On  what  principle  does  it  de- 
pend ? 


176  VELOCITY    OF    LIGHT. 

| 

accuracy  by  the  eye.  It  has  been  found  that  eyes  of 
average  sensitiveness  fail  to  distinguish  the  effect  of  a 
light  when  it  is  in  presence  of  another  sixty-four  times  as 
intense.  The  precise  number  varies  somewhat  with  dif- 
ferent eyes ;  but  to  the  same  eye  it  is  always  the  same. 
If  there  be  any  doubt  as  to  the  perfect  disappearance  of 
the  shadow,  the  receiving  screen  may  be  agitated  or 
moved  a  little.  This  brings  the  shadow,  to  a  certain  ex- 
tent, into  view  again.  Its  place  can  then  be  traced  ;  and, 
on  ceasing  the  motion,  the  disappearance  verified. 

When,  therefore,  we  desire  to  discover  the  relative  in- 
tensities of  light,  we  have  merely  to  inquire  at  what  dis- 
tance they  effect  the  total  obliteration  of  a  shadow,  and 
their  intensities  are  as  the  squares  of  those  distances.  I 
have  employed  this  method  for  the  determination  of  the 
quantities  of  light  emitted  by  a  solid  at  different  temper- 
atures, and  have  found  it  very  exact. 

Light  does  not  pass  instantaneously  from  one  point  to 
another,  but  with  a  measurable  velocity.  The  ancients 
believed  that  its  transmission  was  instantaneous,  illustrat- 
ing it  by  the  example  of  a  stick,  which,  when  pushed 
at  one  end,  simultaneously  moves  at  the  other.  They 
did  not  know  that  even  their  illustration  was  false ;  for  a 
certain  time  elapses  before  the  farther  end  of  the  stick 
moves  ;  and,  in  reality,  a  longer  time  than  light  would  re- 
quire to  pass  over  a  distance  equal  to  the  length  of  the 
stick.  But  in  1676,  a  Danish  astronomer,  Roemer,  found, 
from  observations  on  the  eclipses  of  Jupiter's  satellites, 
that  light  moves  at  the  rate  of  about  192,000  miles  in  one 
second. 

This  singular  observation  may  be  explained  as  follows  : 
Let  S,  Fig.  193,  be  the  sun,  E  the  earth,  moving  in  the 
orbit  E  E',  as  indicated  by  the  arrows ;  let  J  be  Jupi- 
ter and  T  his  first  satellite,  moving  in  its  orbit  round 
him.  It  takes  the  satellite  42  hours  28  minutes  35  sec- 
onds to  pass  from  T  to  T' — that  is  to  say,  through  the 
planet's  shadow.  But,  during  this  period  of  time,  the 
earth  moves  in  her  orbit,  from  E  to  E',  a  space  of 
2,880,000  miles.  Now,  it  is  found,  under  these  circum- 

Does  light  move  with  instantaneous  velocity  ?  Who  discovered  its  pro- 
gressive motion  ?  What  is  its  actual  rate  ?  Describe  the  facts  by  which 
tins  has  been  determined.  By  whom  and  under  what  circumstances  has 
this  been  verified  ? 


ROEMER'S  AND  BRADLEY'S  DISCOVERIES.        177 
ptances,  that  the  emersion  of  the  satellite  is  15  seconds 

Fig.  193. 


later  than  it  should  have  been.  And  it  is  clear  that  this 
is  owing  to  the  fact  that  the  light  requires  15  seconds  to 
pass  from  E  to  E'  and  overtake  the  earth.  Its  velocity, 
therefore,  in  one  second,  must  be  192,000  miles. 

This   beautiful    deduction    was    corroborated    by  Dr. 
Bradley,  in  1725,  upon  totally  different  principles,  involv- 
ing what  is  termed  the  aberration  of  the  stars.    The  prin- 
ciple, which  is  somewhat  dif-  Fig.  194. 
ficult  to  explain,  is  clearly  il-  M 
lustrated  by  Eisenlohr  as  fol 
lows :   Let  M  N  represent  a 
ship,  whose  side  is  aimed  at 
point  blank  by  a  cannon  at  a. 
Now,  if  the  vessel  were  at 

rest,  a  ball  discharged  in  this  Mr/ 

manner  would  pass  through 
the  points  b  and  c,  so  that  the 
three  points,  a,  b,  and  c,  would  all  be  in  the  same  straight 
line.  But  if  the  vessel  itself  move  from  M  toward  N, 
then  the  ball  which  entered  at  b  would  not  come  out  at 
the  opposite  point,  c,  but  at  some  other  point,  d,  as  much 
nearer  to  the  stern,  as  is  equal  to  the  distance  gone  over 
by  the  vessel,  from  M  to  N,  during  the  time  of  passage 
of  the  ball  through  her.  The  lines  b  c  and  b  d,  therefore, 
form  an  angle  at  i,  whose  magnitude  depends  on  the  po- 
sition of  b  c  and  b  d.  The  greater  the  velocity  of  the 
ball,  as  compared  with  the  ship,  the  less  the  angle.  Next, 

What  is  meant  by  the  aberration  of  the  fixed  stars  ?  Give  an  illustration 
of  it.  What  is  the  value  of  the  angle  of  aberration  ?  What  is  the  velocity 
of  light  as  thus  determined  ? 


178  REFLEXION    OF    LIGHT. 

for  the  ship  substitute  in  your  mind  the  earth,  and  for  the 
cannon  any  of  the  fixed  stars ;  let  the  velocity,  b  c,  of  the 
cannon-ball  now  stand  for  that  of  light,  and  let  d  c  be  the 
velocity  of  the  earth  in  her  orbit.  The  angle  d  b  c,  is 
called  the  angle  of  aberration.  It  amounts  to  20£  seconds 
for  all  the  stars ;  for  they  all  exhibit  the  same  alteration 
in  their  apparent  position,  being  more  backward  than 
they  really  are  in  the  direction  of  the  earth's  annual  mo- 
tion, as  Bradley  discovered.  By  a  simple  trigonometri- 
cal calculation,  it  appears  from  these  facts  that  the  velo- 
city of  light  is  195,000  miles  per  second,  a  result  nearly 
coinciding  with  the  former. 


LECTURE  XXXVII. 

REFLEXION  OP  LIGHT.  —  Different  kinds  of  Mirrors. — 
General  Law  of  Reflexion. —  Case  of  Parallel,  Con- 
verging, and  Diverging  Rays  on  Plane  Mirrors. —  The 
Kaleidoscope. — Properties  of  Spherical  Concave  Mir- 
rors.— Properties  of  Spherical  Convex  Mirrors. — Spheri- 
cal Aberration. — Mirrors  of  other  Forms. —  Cylindrical 
Mirrors. 

WHEN  a  ray  of  light  falls  upon  a  surfaceAit  may.be 
reflected,  or  transmitted,  or  absorbed./ 

We  therefore  proceed  to  the  study  of  these  three 
incidents,  which  may  happen  to  light,  commencing  with 
reflexion. 

Reflecting  surfaces  in  optics  are  called  mirrors;  they 
are  of  various  kinds,  as  of  polished  metal  or  glass.  They 
differ  also  as  respects  the  figure  of  their  surfaces, \being 
plane,  convex,  or  concave;!  and  again  they  are  divided 
into  such  as  arej  spherical,  parabolic,  elliptical,  &c?) 

The  general  law  which  is  at  the  foundation  of  this 
part  of  optics — the  law  of  reflexion — is  as  follows  : 

The  angle  of  reflexion  is  equal  to  the  angle  of  Incidence, 
the  reflected  ray  is  in  the  opposite  side  of  the  perpendicular, 
and  the  perpendicular,  the  incident,  and  the  reflected  rays 
are  all  in  the  same  plane.  i 

When  a  ray  of  light  falls  on  a  surface  what  may  happen  to  it  1  What  is 
meant  by  reflecting  surfaces?  What  is  the  general  law  of  reflexion? 


PLANE    MIRRORS. 


179 


Thus,  let  c,  Fig.  195,  be  the  reflecting  sur- 
face ;  b  c  a  perpendicular  to  it  at  any  point, 
a  c  a  ray  incident  on  the  same  point ;  the 
path  of  the  reflected  ray  under  the  foregoing 
law  will  be  c  d  ;  such,  that  it  is  on  the  oppo- 
site side  of  the  perpendicular  to  the  incident 
ray,  that  a  c,cb,  and  c  d,  are  all  in  the  same 
plane,  and  that  the  angle  of  incidence,  a  c  b,  is  equal  to 
the  angle  of  reflexion,  bed. 

Reflexion  from  mirror  surfaces  may  be  studied  under 
three  divisions :  reflexion  from  plane,  from  concave,  and 
from  convex  mirrors. 

When  parallel  rays  fall  on  a  plane  mirror,  they  will  be 
reflected  parallel,  and  divergent  and  convergent  rays  will 
respectively  diverge  and  converge  at  angles  equal  to  their 
angles  of  incidence. 

When  rays  diverging  from  a  point  fall  on  a  mirror, 
they  are  reflected  from  it  in  such  a  manner  as  though 
they  proceeded  from  a  point  as  far  behind  it  as  it  is  in 
reality  before  it.  This  principle  has  already  been  ex- 
plained in  Lecture  XXXII,  Fig. 
176.  It  is  illustrated  in  Fig.  196. 
Thus,  if  from  the  point  a  two 
rays,  a  b,  a  c,  diverge,  they  will, 
under  the  general  law,  be  respect- 
ively reflected  along  b  d,  c  e  ;  and 
if  these  be  produced  they  will  in- 
tersect at  a',  as  far  behind  the 
mirror  as  a  is  before  it.  The 
point  a!  is  called  the  virtual  focus,  d; 

From  this  it  appears  that  any 
object  seen  in  a  plane  mirror  ap- 
pears to  be  as  far  behind  it  as  it  is 
in  reality  before  it. 

If  an  object  is  placed  between  two  parallel  plane  mir- 
rors each  will  produce  a  reflected  image,  and  will  also 
repeat  the  one  reflected  by  the  other.  The  consequence 
is,  therefore,  that  there  is  an  indefinite  number  of  images 
produced,  and  in  reality  the  number  would  be  infinite 

Illustrate  this  law  by  Fig.  195.  What  three  kinds  of  mirrors  are  there  ? 
When  parallel,  divergent,  or  convergent  rays  fall  on  a  plane  mirror,  what 
happens  to  them  after  reflexion  ?  What  does  Fig.  196  illustrate  ?  What 
is  the  effect  of  two  parallel  plane  mirrors  ? 


180  CONCAVE    MIRRORS. 

were  the  light  not  gradually  enfeebled  by  loss  at  each 
successive  reflexion. 

The  kaleidoscope  is  a  tube  containing  two  plane  mir- 
rors, which  run  through  it  lengthwise,  and  are  generally 
inclined  at  an  angle  of  60°.  At  one  end  of  the  tube  is  an 
arrangement  by  which  pieces  of  colored  glass  or  other 
objects  may  be  held,  and  at  the  other  there  is  a  cap  with 
a  small  aperture.  On  placing  the  eye  at  this  aperture 
the  objects  are  reflected,  and  form  a  beautiful  hexag- 
onal combination,  their  position  and  appearance  may  be 
varied  by  turning  the  tube  round  on  its  axis. 

Concave  and  convex  mirrors  are  commonly  ground  to 
a  spherical  figure,  though  other  figures,  such  as  ellipsoids, 
parabaloids,  &c.,  are  occasionally  used  for  special  pur- 
poses. It  is  the  properties  of  spherical  concaves  that  we 
shall  first  describe. 

The  general  action  of  a  spherical  mirror  may  be  under- 
197.  stood  by  regarding 

it  as  made  up  of 
a  great  number  of 
small  plane  mirrors, 
as  A,  B,  C,  D,  E, 
FfG,jFV#197.  On 
such  a  combination 
of  small  mirrors,  let 
rays  emanating  from  R  impinge.  The  different  degrees 
of  obliquity  under  which  they  fall  upon  the  mirrors  cause 
them  io  follow  new  paths  after  reflexion,  so  that  they 
converge  to  the  point  S  as  to  a  focus. 

The  problem  of  determining  the  path  of  a  ray  after  it 
has  been  reflected  is  solved  by  first  drawing  a  perpen- 
dicular to  the  surface  at  the  point  of  impact,  and  then 
drawing  a  line  on  the  opposite  side  of  this  perpendicular, 
making  with  it  an  angle  equal  to  that  of  the  angle  of 
incidence  of  the  incident  ray.  Thus,  let  r,  s,  Fig.  198, 
be  an  incident  ray  falling  on  any  reflecting  surface  at  s. 
To  find  the  path  it  will  take  after  reflexion,  we  first  draw 
s  c,  a  perpendicular  to  the  surface  at  the  point  of  impact,  s. 
And  then  draw  the  line  s  f  on  the  opposite  side  of  the 

What  is  the  kaleidoscope  ?  What  is  the  ordinary  figure  of  concave  and 
convex  mirrors  ?  How  may  the  general  action  of  these  mirrors  be  con- 
ceived? Describe  the  method  for  determining  the  path  of  rays  after 
reflexion. 


CONCAVE    MIRRORS.  181 

perpendicular  c  s,  such,  that  the  angle  c  s  f  is  equal  to 
the  angle  c  s  r.  This  is  nothing  but  an  application  of 
the  general  law  of  reflexion,  that  the  angles  of  incidence 
and  reflexion  are  equal  to  one  another,  and  are  on  oppo- 
site sides  of  the  perpendicular. 

When  rays  of  light  diverge  from  the  center  of  a  spheri- 
cal concave  mirror,  after  reflexion  they  converge  back 
to  the  same  point.  For,  from  the  nature  of  such  a  surface, 
lines  drawn  from  its  center  are  perpendicular  to  the  point 
to  which  they  are  drawn,  every  ray,  therefore,  impinges 
perpendicularly  upon  the  surface  and  returns  to  the  center 
again. 

When  parallel  rays  of  light  fall  on  the  surface  of  a  sphe- 
Fig,  198.  rical  mirror,  the  aper- 

r  ture  or  diameter  of 

~  which    is    not    very 
large,    they    are    re- 

fleeted  to  a  point  half 

way  between  the  sur- 

IL face  and  center  of  the 

mirror.  Thus,  let  rs 
ff  s'  be  parallel  rays 
falling  on  the  mirror  s  s',  the  aperture,  s  s',  of  which  is  only 
a  few  degrees,  these  rays,  after  reflexion,  will  be  found 
converging  to  the  point  ft  which  is  called  the  principal 
focus,  half  way  between  the  vertex  of  the  mirror,  v,  and 
its  center,  c;  for  if  we  draw  the  radii,  c  s  c  s',  these  lines 
are  perpendiculars  to  the  mirror  at  the  points  on  which 
they  fall  ;  then  make  the  angles  c  sf  equal  csr,  and  c  s'f 
equal  c  s'  r',  and  it  is  easy  to  prove  that  the  pointy  is 
midway  between  v  and  c. 

But  if  the  aperture,  s  s',  of  the  mirror  exceeds  a  few  de- 
grees, it  may  be  proved  geometrically  that  the  rays  no 
longer  converge  to  the  focus,/)  but,  as  the  aperture  in- 
creases, are  found  nearer  and  nearer  to  the  vertex,  v,  until 
finally,  were  it  not  for  the  opacity  of  the  mirror,  they 
would  fall  at  the  back  of  it.  As  this  deviation  is  depend- 
ent on  the  spherical  figure  of  the  mirror,  it  is  termed 
aberration  of  sphericity. 

When  rays  diverge  from  the  center  of  a  spherical  concave  mirror,  where 
will  they  be  found  after  reflexion  ?  What  is  the  case  when  parallel  rays 
fall  on  a  spherical  mirror  ?  Why  is  the  result  limited  to  mirrors  of  small 
aperture  ?  What  is  meant  by  aberration  of  sphericity  ? 


182 


CONCAVE    MIRRORS. 


Fig.  200. 


Conversely,  if  diverging  rays  issue  from  a  lucid  point, 

f.Fig.  198,  half  way 
between  the  vertex 
and  center  of  a  spheri- 
cal mirror  of  limited 
aperture,  they  will  be 
reflected  in  parallel 
lines. 

Rays  coming   from 
any  point,  rt  Fig.  199, 
at  a  finite  distance  beyond  the  center  of  the  mirror,  will 

be  reflected  so  as  to  fall 
between  the  focus,  f,  and 
the  center,  c. 

Rays  coming  from  a  point, 
r,  Fig.  200,  between  the 
focus,  f,  and  the  vertex,  v, 
will  diverge  after  reflexion. 
Under  such  circumstances 
a  virtual  focus,  f,  exists 
at  the  back  of  the  mirror. 

Concave  mirrors  give  rise 
to  the  formation  of  images 
in  their  foci.  This  fact  may  be  shown  experimentally  by 
placing  a  candle  at  a  certain  distance  in  front  of  such  a  mir- 
ror and  a  small  screen  of  paper  at  the  focus.  On  this  paper 
will  be  seen  an  image  of  the  flame,  beautifully  clear  and 
distinct,  but  inverted.  The  relative  size  and  position  of 
this  image  varies  according  to  the  distance  of  the  object 
from  the  vertex  of  the  mirror. 

The  second  variety  of  curved  mirrors  is  the  convex ; 
their  chief  properties  are  as  follows  : 

When  parallel  rays  fall  on  the  surface  of  a  convex  mir- 
ror, they  become  divergent  after  reflexion  ;  for  let  s  s'  be 
such  a  mirror,  and  r  s  r'  s'  rays  parallel  to  its  axis  falling 
on  it,  let  c  be  the  center  of  the  mirror,  and  draw  c  s  c  s', 
which  wifl  be  respectively  perpendicular  to  the  mirror  at 
the  points  s  and  s' ;  then  for  the  reflected  rays,  make  the 

What  is  the  case  when  diverging  rays  issue  from  the  focus  of  a  spherical 
mirror  ?  What  when  they  come  from  a  finite  distance  beyond  the  center  ? 
What  when  they  come  from  between  the  focus  and  the  vertex  ?  How  may 
it  be  proved  that  concave  mirrors  form  images  ?  What  is  the  second  vari- 
ety of  mirrors  ?  When  parallel  rays  fall  on  a  convex  mirror,  what  path 
do  they  take  ? 


CONVEX    MIRRORS. 


183 


angle,  t  s  p,  equal  to^?  s  r,  and  the  angle,  t'  s'  p't  equal  to 
p'  s'  r'.     It  may  then  jrer.'au. 

be  demonstrated,  that 
not  only  do  these  re- 
flected rays  diverge, 
but  if  they  be  produced 
through  the  mirror  till 
they  intersect,  they  will 
give  a  virtual  focus  at 
~f,  half  way  between 
the  Vertex  of  the  mir- 
ror, v,  and  its  center,  c, 
so  long  as  the  mirror  is 
of  a  limited  aperture. 

In  a  similar  manner 
it  may  be  proved  that  diverging  rays,  falling  on  a  convex 
mirror,  become  more  divergent. 

To  avoid  the  effect  of  spherical  aberration,  it  has  been 
proposed  to  give  to  mirrors  other  forms  than  the  spherical. 
Some  are  ground  to  a  paraboloidal,  and  others  to  an  ellip- 
soidal figure.  .  Of  the  properties  of  such  surfaces  I  have 
already  spoken,  under  the  theory  of  Undulations,  in  Lec- 
ture XXXII ;  and  the  effects  remain  the  same,  whether  we 
consider  light  as  consisting  of  innumerable  small  particles, 
shot  forth  with  great  velocity,  or  of  undulations  arising  in 
an  elastic  ether.  In  both  cases  parallel  rays,  falling  on  a 
paraboloidal  mirror,  are  accurately  converged  to  the  fo- 
cus, whatever  the  aperture  of  the  mirror  may  be  ;  and  in 
ellipsoidal  ones,  rays  diverging  from  one  of  the  foci,  are 
collected  together  in  the  other.  Occasionally,  for  the  pur- 
poses of  amusement,  mirrors  are  ground  to  cylindrical 
or  conical  figures;  they  distort  the  appearance  of  objects 
presented  to  them,  or  reflect,  in  proper  proportions,  the 
images  of  distorted  or  ludicrous  paintings. 

Why  are  paraboloidal  and  ellipsoidal  mirrors  sometimes  used  ?  What 
is  the  effect  of  the  former  on  parallel  rays  I  What  of  the  latter  on  rays  is- 
suing from  one  of  the  foci  ?  What  are  the  effects  of  cylindrical  mirrors  ? 


184  REFRACTION    OF    LIGHT. 


LECTURE  XXXVIII. 

REFRACTION  OF  LIGHT. — Refractive  Action  described. — 
Law  of  the  fines. — Relation  of  the  Refractive  Power 
with  other  Qualities. —  Total  Reflexion.— Rays  on  plane 
Surfaces. —  The  Prism. — Action  of  the  Prism  on  a  Ray. 
— —  The  M.ultiplying-  Glass. 

WHEN  a  ray  of  light  passes  out  of  one  medium  into 
another  of  a  different  density,  its  rectilinear  progress  is 
disturbed,  and  it  bends  into  a  new  path.  This  phenom- 
enon is  designated  the  refraction  of  light. 

Thus,  if  a  sunbeam,  entering  through  a  small  hole  in 
the  shutter  of  a  dark  room,  falls  on  the  surface  of  some 
water  contained  in  a  vessel,  the  beam,  instead  of  passing 
on  in  a  straight  line,  as  it  would  have  done  had  the  water 
not  intervened,  is  bent  or  broken  at  the  point  of  incidence, 
and  moves  in  the  new  direction. 

Fig.  202.  jn  £ne  same  way,  also,  if  a 

coin  or  any  other  object,  O, 
Fig.  202,  be  placed  at  the 
bottom  of  an  empty  bowl, 
A  B  C  D,  and  the  eye  at  E 
so  situated  that  it  cannot  per- 
ceive the  coin,  the  edge  of 
the  vessel  intervening,  if  we 
pour  in  water  the  object  comes 
into  view;  and  the  cause  of  this  is  the  same  as  in  the  for- 
mer illustration  :  for  while  the  vessel  is  empty  the  ray  is 
obstructed  by  the  edge  of  the  bowl,  as  at  O  Gr  E,  but 
when  water  is  poured  in  to  the  height  F  Gr,  refraction 
at  the  point  L,  from  the  perpendicular,  P  Q,  ensues;  and 
now  the  ray  takes  the  course  OLE,  and  entering  the  eye 
at  E,  the  object  appears  at  K,  in  the  line  E  L  K. 

For  the  same  reason  oars  or  straight  sticks  immersed 
in  water  look  broken,  and  the  bottom  of  a  stream  seems 
at  a  much  less  depth  than  what  it  actually  is. 

What  is  meant  by  the  refraction  of  light  ?  Explain  the  illustrations  of 
this  phenomenon  as  given  in  Figs.  202  and  203. 


REFRACTION    OF    LIGHT. 


185 


The  same  result  ensues  under  the  circumstances  repre- 
sented in  Fig.  203,  in  which  E  represents  a  candle,  the 
rays  of  which  fall  on  a  Fv-  2°3- 

rectangular  box,  ABC 
D,  under  such  circum- 
stances as  to  cast  the 
shadow  of  the  side  A  C, 
so  as  to  fall  at  D.  If  the  B 
box  be  now  filled  with 
water,  every  thing  re-  D  3  C 

maining  as  before,  the  shadow  will  leave  the  point  D  and 
go  to  d,  die  rays  undergoing  refraction  as  they  enter  the 
liquid ;  and  if  the  eye  could  be  placed  at  d,  it  would  see 
the  candle  at  e,  in  the  direction  of  d  A  produced. 

Let  N  O,  Fig.  204,  be  a  refracting  surface,  and  C  the 


G  E 

point  of  incidence  of  a  ray,  B  C,  C  E  the  course  of  the 
refracted  ray,  and  C  K  the  course  the  ray  would  have 
taken  had  not  refraction  ensued.  With  the  point  of  inci- 
dence, C,  as  a  center,  describe  a  circle,  N  M  O  G,  and  from 
A  and  R  draw  the  lines  A  D,  R  H  at  right  angles  to  the 
perpendicular  M  G  to  the  point  C.  Then  ACM  will 
be  the  angle  of  incidence,  R  C  G  the  angle  of  refraction ; 
A  D  is  the  sine  of  the  angle  of  incidence,  and  H  R  the 
sine  of  the  angle  of  refraction.  Now  in  every  medium 

Explain  Fig.  204.    What  is  the  angle  of  incidence  ?    What  is  the  angle 
of  refraction  ?    Which  are  the  sines  of  those  angles  ? 


186 


LAW    OF    SINES. 


Fig.  205. 


these  lines  have  a  fixed  relation  to  one  another,  and  the 
general  law  of  refraction  is  as  follows  : — 

In  each  medium  the  sine  of  the  angle  of  incidence  is  in  a 
constant  ratio  to  the  sine  of  the  angle  of  refraction  ;  the  in- 
cident, the  perpendicular,  and  the  refracted  ray  are  all  in 
the  same  place,  which  is  always  at  right  angles  to  the  plane 
of  the  refracting  medium. 

To  a  beginner,  this  law  of 
the  constancy  of  sines  may  be 
explained  as  follows  : — Let  C 
D,  Fig.  205,  be  a  ray  falling 
on  a  medium,  A  B,  in  the  point 
D,  where  it  undergoes  refrac- 
tion and  takes  the  direction  D 
,E.  Its  sine  of  incidence,  as 
just  explained,  is  C  g,  and  its 
sine  of  refraction  E  e;  and  let 
us  suppose  that  the  medium  is 
of  such  a  nature  that  the  sine 
of  refraction  is  one  half  the  sine  of  incidence— that  is,  E 
e  is  half  C  g.  Moreover,  let  there  be  a  second  ray,  H  D, 
incident  also  at  the  point  D,  and  refracted  along  D  F ; 
H  h  will  be  its  sine  of  incidence,  and  F  f  its  sine  of  re- 
fraction;  and  by  the  law  Ff  will  be  exactly  one  half  HA. 
The  proportion  or  relation  between  these  sines  differs 
when  different  media  are  used,  but  for  the  same  medium 
it  is  always  the  same.  Thus,  in  the  case  of  water,  the  pro- 
portion is  as  1.366  to  1;  for  flint-glass,  1.584  to  1;  for  dia- 
mond, 2.487  to  1.  These  numbers  are  obtained  by  ex- 
periment. They  are  called  the  indices  of  refraction  of 
bodies,  and  tables  of  the  more  common  substances  are 
given  in  the  larger  works  on  optics. 

No  general  law  has  as  yet  been  discovered  which  would 
enable  us  to  predict  the  refractive  power  of  bodies  from 
any  of  their  other  qualities;  but  it  has  been  noticed  that 
inflammable  bodies  are  commonly  more  powerful  than 
incombustible  ones,  and  those  that  are  dense  are  more  en- 
ergetic than  those  that  are  rare. 

When  a  ray  of  light  passes  out  of  a  rare  into  a  dense 

What  relation  do  these  sines  bear  to  one  another  ?  Explain  the  law  of 
the  constancy  of  the  sines  as  given  in  Fig.  205.  What  is  the  rate  for  water, 
flint-glass,  and  diamond  ?  What  is  meant  by  indices  of  refraction  ?  Is  the 
refractive  power  of  bodies  connected  with  any  other  property  ? 


TOTAL    REFLEXION.  187 

medium,  it  is  refracted  toward  the  perpendicular.  Fig. 
203  is  an  illustration — the  rays  passing  from  air  into  wa- 
ter. But  when  a  ray  passes  from  a  dense  into  a  rarer 
medium  it  is  refracted  from  the  perpendicular.  Fig. 
202  is  an  example — the  rays  passing  from  water  into 
air. 

In  every  case  when  a  ray  falls  on  the  surface  of  any 
medium  whatever,  it  is  only  a  portion  which  is  transmit- 
ted, a  portion  being  always  reflected.  If  in  a  dark  room 
we  receive  a  sunbeam  on  the  surface  of  some  water,  this 
division  into  a  reflected  and  a  refracted  ray  is  very  evi- 
dent :  and  when  a  ray  is  about  to  pass  out  of  a  highly  re- 
fractive medium  into  one  that  is  less  so,  making  the  angle 
of  incidence  so  large  th.at  the  angle  of  refraction  is  equal 
to  or  exceeds  90°,  total  reflexion  ensues.  This  may  be 
readily  shown  by  allowing  the  .  Fig.  206. 

rays  from  a  candle,  ft  or  any  .^ 

other  object,  to  fall  on  the  sec- 
ond face,  b  c,  of  a  glass  prism,  a  & 
b  c,  Fig.  2Q6 ;  the  eye  placed  atd 
will  receive  the  reflected  ray,  d 
e,  and  it  will  be  perceived  that 
the  face  b  c  of  the  glass,  when 
exposed  to   the   daylight,    ap- 
pears  as  though   it  were    sil- 
vered,   reflecting    perfectly    all   objects  exposed    to   its 
front,  a  c. 

As  with  the  reflexion  of  light,  so  with  refraction — it  is 
to  be  considered  as  taking  place  on  plane,  convex,  and 
concave  surfaces. 

When  parallel  rays  fall  upon  a  plane  refracting  surface 
they  continue  parallel  after  refraction.  This  must  neces- 
sarily be  the  case  on  account  of  the  uniform  action  of  the 
medium. 

If  divergent  rays  fall  upon  a  plane  of  greater  refractive 
power  than  the  medium  through  which  they  have  come, 
they  will  be  less  divergent  than  before.  Thus,  from  the 
point  a  let  the  rays  a  b,  a  b'  diverge ;  after  suffering  re- 
fraction they  will  pass  in  the  paths  b  c,  b'  c',  and  if  these 

When  is  light  refracted  toward  and  when  from  the  perpendicular  ?  Is 
the  whole  of  the  light  transmitted '(  Under  what  circumstance  does  total 
reflexion  take  place  ?  What  ensues  when  parallel  rays  fall  on  a  plane 
surface  ?  What  is  the  case  with  diverging  ones  ? 


188  THE    PRISM. 

lines  be  projected,  they  will  inter- 
sect at  a',  but  a'  b,  a'  b'  are  less 
divergent  than  a  b,  a  b'. 

If,  on  the  contrary,  rays  pass 
from  a  medium  of  greater  to  one 
of  less  refractive  power,  they  will 
be  more  divergent  after  refrac- 
tion. For  this  reason  bodies  un- 
der water  appear  nearer  the  sur- 
face than  they  actually  are. 

When  parallel  rays  of  light  pass 
through  a  medium  bounded  .by 
planes  that  are  parallel,  as  through 
a  plate  of  glass,  they  will  continue 
still  parallel  to  one  another,  and  to  their  original  direction, 
after  refraction.  For  this  reason,  therefore,  we  see  through 
such  plates  of  glass  objects  in  their  natural  positions  and 
relation. 

The  optical  prism  is  a  transparent  medium,  having 
Fig.  208.  plane  surfaces  inclined  to  one  another.  It  is 
usually  a  wedge-shaped  piece  of  glass,  a  a, 
a  Fig.  208,  which  can  be  turned  into  any  suita- 
ble position,  on  a  ball  and  socket-joint,  c,  and 
is  supported  on  a  stand,  b.  As  this  instrument 
is  of  great  use  in  optical  researches,  we  shall 
describe  the  path  of  a  ray  of  light  through,  it 
more  minutely. 

Let,  therefore,  ABC,  Fig.  209,  be  such  a  glass  prism 
Fiz- 209-  seen  endwise,  and  let 

a  b  be  a  ray  of  light 
incident  at  b.  As  this 
ray  is  passing  from  a 

\~^K  rarer  to  a  denser  me- 

dium   it   is    refracted 
c  toward  the  perpendic- 

••'"*&'  ular  to  an  extent  de- 

pendent on  the  refractive  power  of  the  glass  of  which  the 
prism  is  composed,  and  therefore  pursues  a  new  path,  b 
c,  through  the  glass ;  at  c  it  again  undergoes  refraction, 
and  now  passing  from  a  denser  to  a  rarer  medium,  takes 

What  is  the  case  when  parallel  rays  pass  through  media  with  plane  and 
parallel  surfaces  ?  What  is  a  prism  ?  Describe  the  path  of  a  ray  of  light 
through  this  instrument. 


MULTIPLYING-GLASS. 


189 


Fig,  210. 


a  new  course,  c  d.  To  an  eye  placed  at  d,  and  looking 
through  the  prism,  an  object,  a,  seems  as  though  it  were 
at  a',  in  the  straight  line  d  c  continued.  Through  this  in- 
strument, therefore,  the  position  of  objects  is  changed, 
the  refracted  ray,  c  d,  proceeding  toward  the  back,  A  B, 
of  the  prism. 

But  the  prism  in  actual  practice  gives  rise  to  far  more 
complicated  and  interesting  effects,  to  be  described  here- 
after, when  we  come  to  speak  of  the  colors  of  light. 

The  multiplying-glass  is  a 
transparent  body,  having  sever- 
al inclined  faces.  Its  construc- 
tion and  action  are  represented 
at  Fig.  210.  Let  A  B  be  a 
plane  face,  C  D  also  plane  and 
parallel  to  it,  but  A  C  and  D  B 
inclined.  Now  let  rays  come 
from  any  object,  a,  those,  a  b, 
which  fall  perpendicularly  on 
the  two  faces  will  pass  with- 
out suffering  refraction ;  but 
those,  ac,  a  d,  which  fall  on  the 
inclined  faces  will  be  refracted 
into  new  paths,  c  f,  d  f,  these 
portions  acting  like  the  prism  heretofore  described.  Con- 
sequently, an  eye  placed  aty*  will  see  three  images  of  the 
object  in  the  direction  of  the  lines  along  which  the  rays 
have  come — that  is,  at  a',  a,  a".  Hence  the  term  multi- 
plying-glass, because  it  gives  as  many  images  of  an  ob- 
ject as  it  has  inclined  surfaces. 

To  what  other  phenomenon  does  the  prism  give  rise  ?  What  is  the 
multiplying-glass?  Why  does  it  give  as  many  images  of  an  object  as  it 
has  faces  ? 


190 


LENSES. 


LECTURE  XXXIX. 

THE  ACTION  OP  LENSES. — Different  Forms  of  Lenses. — 
General  Properties  of  Convex  Lenses. — General  Proper- 
ties of  Concave  Lenses. — Analogy  between  Mirrors  and 
Lenses. — Production  of  Images  by  Lenses. — Size  and 
Distance  of  Images. —  Visual  Angle. — Magnifying  Ef- 
fects.— Burning -Lenses. 

TRANSPARENT  media  having  curved  surfaces  are  called 
lenses.     They  are  of  six  Fig.  211. 

different  kinds,  as  repre-  A  .^MMiiMsi^  Plano-convex. 
sentedin  Fig.  211.'  The 
plano-convex  lens,  A,  has  B 
one  surface  plane  and  the 
other  convex,  the  plano- 
concave, B,  has  one  sur- 
face plane  and  the  other 
concave  ;  C  is  the  double 
convex,  I)  the  double  con- 
cave, E  the  meniscus,  and 
F  the  concavo-convex. 


Plano-concave. 
Double  Convex. 
Double  Concave. 


Meniscus. 
Concavo-convex. 


For  optical  uses  lenses  are  commonly  made  of  glass, 
but  for  certain  purposes  other  substances  are  employed. 
For  example,  rock  crystal  is  often  used  for  making  spec- 
tacle lenses ;  it  is  a  hard  substance,  and  is  not,  therefore, 
so  liable  to  be  scratched  or  in- 
jured as  glass. 

In  a  lens  the  point  c  is  called 
the  geometrical  center,  for  all 
lenses  are  ground  to  spherical 
surfaces,  and  c  is  the  center  of 
their  curvature  ;  the  aperture  of 
the  lens  is  a  b,  and  d  is  its  opti- 
cal center  ;  f  e  is  the  axis,  and  any 
ray,  m  n,  which  passes  through 
the  optical  center,  is  called  a  principal  ray. 

What  are  lenses  ?  How  many  kinds  of  lenses  are  there  ?  What  are 
they  commonly  made  of?  What  other  substances  are  sometimes  used  ? 
What  is  the  geometrical  center  ?  What  is  the  optical  center  ?  What  is 
a  principal  ray  ?  What  is  the  aperture  ? 


ACTION    OP    LENSES. 


191 


The  general  action  of  lenses  of  all  kinds  may  be  under- 
stood after  what  has  been  said  in  relation  to  the  prism,  of 
•which  it  was  remarked  that  the  refracted  ray  is  bent  toward 
the  back.  Thus,  if  we  have  Fig.  213. 

two  prisms,  a  c  e,  b  c  e, 
placed  back  to  back,  and 
allow  parallel  rays  of  light,  m 
m  n,  to  fall  upon  them, 
these  rays,  after  refraction, 
being  bent  from  their  par- 
allel path  toward  the  back  JT 
of  each  prism,  will  inter- 
sect each  other  in  some 
point,  as  f.  Now,  there  is  obviously  a  strong  analogy 
between  the  figure  of  the  double  convex  lens  and  that  of 
these  two  prisms;  indeed,  the  former  might  be  regarded 
as  a  series  of  prisms  with  curved  surfaces,  and  from  such 
consideration  it  is  clear,  that  when  parallel  rays  fall  on  a 
convex  lens,  they  will  converge  to  a  focal  point. 

Again,  let  us  suppose  that  a  pair  of  prisms  be  placed 
edge  to  edge,  as  shown  in  Fig.  214,  and  that  parallel 
rays,  m  n,  are  incident  upon  them.  These  rays  undergo 
refraction,  as  before,  to-  fig  214 

ward  the  back  of  their  re- 
spective prisms,  b  c,  d  e, 
and  therefore  emerge  di- 
vergent, as  at  f  and  g.  n 
Now,  there  is  an  analogy 
between  such  a  combina- 
tion of  prisms  and  a  con- 
cave lens,  and  we  there- 
fore see  that  the  general 
action  of  such  a  lens  upon 
parallel  rays  is  to  make 
them  divergent. 

By  the  aid  of  the  law  of  refraction  it  may  be  proved 
that  lenses  possess  the  following  properties. 

Every  principal  ray  which  falls  upon  a  convex  lens  of 
limited  thickness  is  transmitted  without  change  of  direc- 
tion. 

How  may  the  general  action  of  a  double  convex  lens  be  deduced  from 
that  of  a  pair  of  prisms  ?  Trace  the  same  action  in  the  case  of  a  double 
concave  lens. 


192  PROPERTIES    OF    LENSES. 

Rays  parallel  to  the  axis  of  a  double  equi-convex  glass 
lens  are  brought  to  a  focus  at  a  distance  from  the  optical 
center  equal  to  the  radius  of  curvature  of  the  lens.  But 
if  it  be  a  plano-convex  glass  the  focal  distance  is  twice  as 
great.  The  focus  for  parallel  rays  is  called  the  principal 
focus. 

Rays  diverging  from  the  principal  focus  of  a  convex 
lens  after  refraction  become  parallel. 

Rays  diverging  from  a  point  in  the  axis  more  distant 
than  the  principal  focus  converge  after  refraction,  their 
point  of  convergence  being  nearer  the  lens  as  the  point 
from  which  they  radiated  was  more  distant. 

Rays  coming  from  a  point  in  the  axis  nearer  than  the 
principal  focus  diverge  after  refraction. 

With  respect  to  concave  lenses,  the  chief  properties 
may  be  described  as  follows  : — 

Every  principal  ray  passes  without  change  of  direction. 
Fig.  215.  Rays  parallel  to  the 

axis  are  made  diver- 
gent. Thus,  m  n,  Fig- 
ure 215,  being  paral- 
lel rays  falling  on  the 
double  concave,  a  b, 
diverge  after  refrac- 
tion in  the  directions 
g  d  ;  and  if  they  be 
produced  give  rise  to 
a  virtual  or  imaginary 
focus  at  f. 

By  concave  lenses  diverging  rays  are  made  still  more 
divergent. 

When  the  effects  of  lenses  are  compared  with  those  of 
mirrors,  it  will  be  found  that  there  is  an  analogy  in  the 
action  of  concave  mirrors  and  convex  lenses,  and  of  con- 
vex mirrors  and  concave  lenses. 

It  has  already  been  remarked  that  concave  mirrors 
give  images  of  external  objects  in  their  focus.  The  same 
holds  good  for  convex  lenses.  Thus,  if  we  take  a  convex 
lens,  and  place  behind  it,  at  the  proper  distance,  a  paper 
screen,  we  shall  find  upon  that  screen  beautiful  images  of 

What  are  the  chief  properties  of  convex  lenses  ?  What  are  the  chief 
properties  of  concave  lenses  ?  What  is  the  relation  between  mirrors  and 
lenses  in  their  effects  ? 


FORMATION    OF    IMAGES.  193 

all  the  objects  in  front  of  the  lens  in  an  inverted  position. 
The  manner  in  which  they  form  may  be  understood  from 
Fig.  216.  Where  L'  L  is  a  double  convex  lens,  M  N 

Fig.  216. 


any  object,  as  an  arrow,  in  front  of  it,  the  lens  will  give 
an  inverted  image,  n  m,  of  the  object  at  a  proper  distance 
behind.  From  the  point  M  all  the  rays,  as  M  L,  M  C, 
M  L',  after  refraction,  will  converge  to  a  focus,  m  ;  and 
from  the  point  N  all  rays,  as  N  L,  N  C,  N  I/,  will  like- 
wise converge  to  a  focus,  n;  and  so,  for  every  interme- 
diate point  between  M  and  N,  intermediate  foci  will  form 
between  m  and  n,  and  therefore  conjointly  give  rise  to 
an  inverted  image. 

The  images  thus  given  by  lenses  or  mirrors  may  be 
made  visible  by  being  received  on  white  screens  or  on 
smoke  rising  from  a  combustible  body,  or  directly  by  the 
eye  placed  in  a  proper  position  to  receive  the  rays.  They 
then  appear  as  if  suspended  in  the  air,  and  are  spoken  of 
as  aerial  images. 

The  distance  of  such  images  from  a  lens,  and  also  their 
magnitude,  vary  with  circumstances. 

If  the  object  be  very  remote,  it  gives  a  minute  image 
in  the  focus  of  the  lens ;  as  it  is  brought  nearer,  the  im- 
age recedes  farther,  and  becomes  larger ;  when  it  is  at  a 
distance  equal  to  twice  the  focal  distance,  the  image  is 
equidistant  from  the  lens  on  the  opposite  side,  and  is  of 
the  same  size  as  the  object.  As  the  object  approaches  still 
nearer,  the  image  recedes,  and  now  becomes  larger  than 
the  object.  When  it  reaches  the  focus,  the  image  is  at 
an  infinite  distance,  the  refracted  rays  being  parallel  to 
one  another.  And,  lastly,  when  the  object  comes  be- 
tween the  focus  and  the  surface  of  the  leils,  an  erect  and 

Do  convex  lenses  give  rise  to  the  formation  of  images  ?  How  does  this 
effect  arise  ?  How  may  such  images  be  made  visible  ?  Under  what 
circumstances  do  the  size  and  distance  of  the  image  vary  ? 

I 


194  MAGNIFYING    POWER. 

magnified  image  of  the  object  will  appear  on  the  same 
side  of  the  lens  as  the  object  itself.  Hence,  convex  lenses 
are  called  magnifying-glasses. 

From  these  considerations,  it  therefore  appears  that  the 


magnifying  power  of  lenses  is  not,  as  is  often  popularly 
supposed,  due  to  the  peculiar  nature  of  the  glass  of 
which  they  are  made,  but  to  the  figure  of  their  surfaces. 
The  dimensions  of  all  objects  depend  on  the  angles  under 
which  they  are  seen.  A  coin  at  a  distance  of  100  yards 
appears  of  very  small  size,  but  as  it  is  brought  nearer  the 
eye  its  size  increases ;  and  when  only  a  few  inches  off,  it 
can  obstruct  the  view  of  large  objects.  Thus,  if  A  rep- 
resent its  size  at  a  remote  distance,  the  angle  D  E  F,  or 
the  visual  angle,  is  the  angle  under  which  it  is  seen  ;  when 
brought  nearer,  at  B,  the  angle  is  Gr  E  H ;  and  at  C,  in- 
creases to  I  E  K.  In  all  cases  the  apparent  size  of  an 
object  increases  as  the  visual  angle  increases,  arid  all  ob- 
jects become  smaller  as  their  distances  increase  ;  and 
any  optical  contrivances,  either  of  lenses  or  mirrors,  which 
can  alter  the  angle  at  which  rays  enter  the  eye  and  make 
it  larger  than  it  would  otherwise  be,  magnify  the  objects 
seen  through  them. 

On  these  principles  concave  mirrors  and  convex 
lenses  magnify,  and  convex  mirrors  and  concave  lenses 
minify. 

From  their  property  of  converging  parallel  rays  to  a  fo- 
cus, convex  lenses  and  concave  mirrors  have  an  interesting 
application,  being  used  for  the  production  of  high  temper- 
atures, by  converging  the  rays  of  the  sun.  Fig.  218  repre- 
sents such  a  burning-glass.  The  parallel  rays  of  the  sun 

Why  are  convex  lenses  magnifying-glasses  ?  On  what  does  this  mag- 
nifying action  depend  ?  What  is  the  visual  angle  of  an  object  ? 


COLORED    LIGHT. 


195 


Fig.  218. 


falling  on  it  are  made  to  con- 
verge, and  this  convergence 
might  be  increased  by  a  sec- 
ond smaller  lens.  *At  the 
focal  point  any  small  object 
being  exposed  its  tempera- 
ture is  instantly  raised.  In 
such  a  focus  there  are  few  sub- 
stances that  can  withstand  the 
heat — brick,  slate,  and  other 
such  earthy  matters  instantly 
boil,  metals  melt,  and  even 
volatilize  away.  During  the 
last  century  some  French  chemists,  using  one  of  these 
instruments,  found  that  when  a  piece  of  silver  is  held 
over  gold,  fused  at  the  focus,  it  became  gilded  over  by 
the  vapor  that  rose  from  the  melted  mass.  And  in  the 
same  way  gold  could  be  whitened  by  the  vapors  of  melt- 
ed silver.  The  heat  attained  in  this  way  far  exceeds  that 
of  the  best  constructed  furnace. 


LECTURE' XL. 

OP  COLORED  LIGHT. — Action  of  the  Prism. — Refraction 
and  Dispersion. —  The  Solar  Spectrum. — Its  Constituent 
Rays. —  They  pre-exist  in  White  Light. —  Theory  of  the 
Different  Rcfrangibility  of  the  Rays  of  Light. — Differ- 
ent Dispersive  Powers. — Irrationality  of  Dispersion. — 
Illuminating  Effects.  —  The  Fixed  Lines.  —  Calorific 
Effects. — Chemical  Effects. 

IN  speaking  of  the  action  of  a  prism,  in  Lect.  XXXVIII., 
it  was  observed,  that  it  gives  rise  to  many  interesting 
results  connected  with  colored  lights.  These,  which  con- 
stitute one  of  the  most  splendid  discoveries  of  Newton,  I 
next  proceed  to  explain. 

Through  an  aperture,  a,  Fig.  219,  in  the  shutter  of  a  dark 
room  let  a  beam  of  light,  a  e,  enter,  and  let  it  be  inter- 
cepted at  some  part  of  its  course  by  a  glass  prism,  seen 

What  is  a  burning  glass  ?  Why  does  it  give  rise  to  the  production  of 
an  intense  heat  ?  Mention  some  of  the  effects  which  have  been  obtained 
by  these  instruments.  Describe  the  action  of  a  prism  on  a  ray  of  light. 


196 


DECOMPOSITION    OF    LIGHT. 


endwise  at  b  c. 

Fig.  219. 


The  light  will  undergo  refraction,  and 
in  consequence  of  what  has  been  al- 
ready stated,  will  pass  in  a  direction, 
d,  toward  the  back  of  the  prism. 

Now,  for  any  thing  that  has  yet 
d  been  said,  it  might  appear  that  this 
refracted  ray,  on  reaching  the  screen 
d  e,  would  form  upon  it  a  white  spot 
similar  to  that  which  it  would  have 
given  at  e,  had  not  the  prism  inter- 
vened. But  when  the  experiment  is 
made,  instead  of  the  light  going  as  a  single  pencil  of  uni- 
form width,  it  spreads  out  into  a  fan  shape,  as  is  indicated 
by  the  dotted  lines,  and  forms  on  the  screen  an  oblong 
image  of  the  most  splendid  colors. 

In  this  beautiful  result,  two  facts,  which  are  wholly 
distinct,  must  be  remarked  :  1st,  the  light  is  refracted 
or  bent  out  of  its  rectilinear  path  ;  2d,  it  is  dispersed  into 
an  oblong  colored  figure. 

On  examining  this  figure  or  image,  which  passes  under 
the  name  of  the  solar  spectrum,  we  find  it  divided  into 
seven  well-marked  regions.  Its  lowest  portion,  that  is  to 
say,  the  part  nearest  to  that  to  which  the  light  would  have 
gone  had  not  the  prism  intervened,  is  of  a  red  color,  the 
most  distant  is  of  a  violet,  and  between  'these  other  colors 
may  be  seen  occurring  in  the  following  order : — 


Fig.  220. 


Red, 
Orange, 
Yellow, 
Green, 


Blue, 

Indigo, 
Violet. 


truth 


In  Fig.  220,  the  order  in  which  they  occur  is 
[indicated  by  their  initial  letters,  e  being  the  point 
to  which  the  light  would  have  gone  had  not  the 
prism  intervened. 

Now,  from  what  source  do  these  splendid  colors 
come  I  Newton  proved  that  they  pre-existed  in 
the  white  light,  which,  in  reality,  is  made  up  of 
I  them  all  taken  in  proper  proportions. 

There  are  many  ways  in  which  this  important 
can  be   established.     Thus,   if  we   take   a  second 


Is  the  refracted  light  white  ?  What  two  general  facts  are  to  he  observ- 
ed ?  What  color  is  the  lowest  portion  of  the  spectrum  ?  What  is  the 
color  of  the  highest.  What  is  the  order  of  the  colors  ? 


DECOMPOSITION    OP    LIGHT. 


197 


Fig.  221. 


prism,  B  B'  S',  Fig. 
221,  and  put  it  in  an  in- 
verted position,  as  re- 
spects the  first,  A  A' S, 
so  that  it  shall  refract 
again  in  the  opposite 
direction  the  rays  re- 
fracted by  the  first, 
they  will,  after  this 
second  refraction,  reunite  and  form  a  uniform  beam,  M, 
of  white  light,  in  all  respects  like  the  original  beam  itself. 

If  the  production  of  color  were  due  to  any  irregular 
action  of  the  faces  of  the  first  prism,  the  introduction  of 
two  more  faces  in  the  second  prism  would  only  tend  to 
increase  the  coloration.  But  so  far  from  this,  no  sooner 
is  this  second  prism  introduced  than  the  rays  reunite  and 
recompose  white  light.  It  follows  as  an  inevitable  conse- 
quence that  ichite  light  contains  all  the  seven  rays. 

But  Newton  was  not  satisfied  with  this.  He  further 
collected  the  prismatic  colored  rays  together  into  one 
focus  by  means  of  a  lens,  and  found  that  they  produced 
a  spot  of  dazzling  whiteness.  And  when  he  took  seven 
powders,  of  colors  corresponding  to  the  prismatic  rays, 
and  ground  them  intimately  together  in  a  mortar,  he 
found  that  the  resulting  powder  had  a  whitish  aspect ;  or 
if,  on  the  surface  of  a  wheel  which  could  be  made  to  spin 
round  very  fast  on  its  axis,  colored  spaces  were  painted, 
when  the  wheel  was  made  to  turn  so  that  the  eye  could 
no  longer  distinguish  the  separate  tints,  the  whole  as- 
sumed a  whitish-gray  appearance. 

By  many  experiments  Newton  proved  that  the  true 
cause  of  this  development  of  brilliant  colors  from  a  ray 
of  white  light  by  the  prism,  is  due  to  the  fact  that  j&afcin- 
strument  does  not  refract  all  the  colors  alike.  Thus,  it 
could  be  completely  shown,  in  the  case  of  any  transparent 
medium,  that  the  violet-ray  was  far  more  refrangible  than 
the  red,  or  more  disturbed  by  such  a  medium  from  its 
course.  In  this  originated  the  doctrine  of  "  the  different 
refraugibility  of  the  rays  of  light." 

How  may  it  be  proved  by  two  prisms  that  all  these  colors  pre-exist  in 
white  light  ?  What  may  be  proved  by  reuniting  the  rays  by  a  lens  ?  What 
by  colored  powders  or  a  painted  wheel?  What  is  the  cause  of  this  de- 
velopment of  colors? 


198  IRRATIONALITY    OF    DISPERSION. 

On  examining  the  order  of  colors  in  the  spectrum,  we 
find,  in  reality,  as  in  Fig.  220,  that  the  red  is  least  dis- 
turbed from  its  course,  and  the  other  colors  follow  in  a 
fixed  order.  The  red,  therefore,  is  spoken  of  as  the  least 
refrangible  ray,  the  violet  as  the  most,  and  the  other  col- 
ors as  intermediately  refrangible. 

We  now  see  the  cause  of  the  development  of  these  col- 
ors from  white  light,  which  contains  them  all.  If  the 
prism  acted  on  every  ray  alike,  it  would  merely  produce 
a  white  spot  at  d,  analogous  to  that  at  e,  Fig.  220,  but  as 
it  acts  unequally  it  separates  the  colored  rays  from  one 
another,  and  gives  rise  to  the  spectrum. 

On  examining  prisms  of  different  transparent  media,  we 
find  that  they  act  very  differently — some  dispersing  the 
rays  far  more  powerfully  than  others  and  giving  rise,  un- 
der the  same  circumstances,  to  spectra  of  very  different 
lengths.  In  the  treatises  on  optics,  tables  of  the  disper- 
sive powers  of  different  transparent  bodies  are  given  : 
thus  it  appears  that  oil  of  cassia  is  more  dispersive  than 
rock-salt,  rock-salt  more  than  water,  and  water  more  than 
flu  or  spar. 

Moreover,  in  many  instances  it  has  been  found  that  if 
we  use  different  prisms  which  give  spectra  of  equal  lengths, 
the  colored  spaces  are  unequally  spread  out.  This  shows 
that  media  differ  in  their  refracting  action  upon  particu- 
lar rays,  some  acting  upon  one  color  more  powerfully 
than  another.  This  is  called  irrationality  of  dispersion. 

The  different  colored  rays  of  light  are  not  equally  lu- 
minous— that  is  to  say,  do  not  impress  our  eyes  with  an 
equal  brilliancy.  If  a  piece  of  finely-printed  paper  be 
placed  in  the  spectrum,  we  can  read  the  letters  at  a  much 
greater  distance  in  the  yellow  than  in  the  other  regions, 
and  from  this  the  light  declines  on  either  hand,  and  grad- 
ually fades  away  in  the  violet  and  the  red. 

It  has  also  been  found  that  the  colors  are  not  continu- 
ous throughout,  but  that  when  delicate  means  of  examina- 
tion are  resorted  to  the  spectrum  is  seen  to  be  crossed  with 
many  hundreds  of  dark  lines,  irregularly  scattered  through 
it.  A  representation  of  some  of  the  larger  of  these  is 

To  what  doctrine  did  this  discovery  give  rise  ?  Do  different  media  dis- 
perse to  the  same  or  different  extents  ?  What  is  meant  by  irrationality 
of  dispersion  ?  Are  all  the  rays  equally  luminous  to  the  eye  ?  How  may 
this  be  proved  ? 


FIXED    LINES.  199 

given  in  Fig.  222.     It  is  curious  that  though  they  exist  in 
the  sun-light,  and  in  that  of  the  planets,  they  are  1^.222. 
not  found  in  the  spectra  of  ordinary   artificial  I™" 
lights;  and,  indeed,  the  electric  spark  gives  a  light 
which  is  crossed  by  brilliant  lines  instead  of  black 
ones.     The  chief  fixed  lines  are  designated  by  the 
letters  of  the  alphabet,  as  shown  in  the  figure. 

The  light  of  the  sun  is  accompanied  by  heat. 
Dr.  Herschel  found  that  the  different  colored  pris- 
matic spaces  possess  very  different  power  over  I 
the  thermometer.  The  heat  is  least  in  the  violet,' 
and  continually  increases  as  we  descend  through 
the  colors,  the  red  being  the  hottest  of  them  all. 
But  below  this,  and  out  of  the  spectrum,  when 
there  is  no  light  at  all,  the  maximum  of  heat  is] 
found.  The  heat  of  the  sunbeam  is,  therefore,  re-  j 
frangible,  but  is  less  refrangible  than  the  red  ray 
of  light. 

Late  discoveries  have  shown  that  every  ray  of  light  can 
produce  specific  changes  in  compound  bodies.  Thus 
it  is  the  yellow  ray  which  controls  the  growth  of  plants, 
and  makes  their  leaves  turn  green;  the  blue  ray  which 
brings  about  a  peculiar  decomposition  of  the  iodides  and 
chlorides  of  silver,  bodies  which  are  used  in  photogenic 
drawing.  Those  substances  which  phosphoresce  after  ex- 
posure to  the  sun  are  differently  affected  by  the  different 
rays — the  more  refrangible  producing  their  glow,  and  the 
less  extinguishing  them. 

Describe  the  fixed  lines  of  the  spectrum.  How  are  they  distinguished  ? 
What  are  the  calorific  effects  of  the  spectrum  ?  Which  is  the  hottest 
space  ?  What  are  the  chemical  effects  ? 


200 


HOMOGENEOUS    LIGHT. 


LECTURE  XLI. 

OF  COLORED  LIGHT. — Properties  of  Homogeneous  Light. — 
Formation  of  Compound  Colors. — Chromatic  Aberration 
of  Lenses. — Achromatic  Prism. — Achromatic  Lens. — 
Imperfect  Achromaticity  from  Irrationality  of  Disper- 
sion.— Cause  of  the  Colors  of  Opaque  Objects. — Effects  of 
Monochromatic  Lights. —  Colors  of  Transparent  Media. 

EACH  color  of  the  prismatic  spectrum  consists  of  homo- 
geneous light.  It  can  no  longer  be  dispersed  into  other 
colors,  or  changed  by  refraction  in  any  manner.  Thus, 

Fig.  223. 


let  a  ray  of  light,  S,  Fig.  223,  enter  through  an  aperture, 
F,  into  a  dark  room,  and  be  dispersed  by  the  prism,  A  B 
C  ;  through  a  hole,  G,  in  a  screen,  D  E,  let  the  resulting 
spectrum  pass,  and  be  received  on  a  second  screen,  d  e, 
placed  some  distance  behind;  in  this  let  there  be  a  small 
opening,  g,  through  which  one  of  the  colored  rays  of  the 
spectrum,  formed  by  A  B  C,  may  pass  and  be  received 
on  a  second  prisrn,  a  b  c.  It  will  undergo  refraction,  and 
pass  to  the  position  M  on  the  screen,  N  M.  But  it  will 
not  be  dispersed,  nor  will  new  colors  arise  from  it ;  and 
it  is  immaterial  which  particular  ray  is  made  to  pass  the 
opening  at  g,  the  same  result  is  uniformly  obtained. 

Homogeneous  or  monochromatic  colors,  therefore,  can- 
not suffer  dispersion. 

By  the  aid  of  the  instrument  Fig.  224,  which  consists 

How  may  it  be  proved  that  homogeneous  light  undergoes  no  further  dis- 
persion ?  What  is  the  use  of  the  instrument  represented  in  Fig.  224  ? 


COMPOUND    COLORS.  201 

of  a  series  of  little  plane  mirrors  set  upon  a  frame,  we 

fig.  224. 


can  demonstrate,  in  a  very  striking  manner,  the  constitu- 
tion of  different  kinds  of  lights  ;  for  if  this  instrument  be 
placed  in  such  a  manner  as  to  receive  the  prismatic  spec- 
trum, by  turning  its  mirrors  in  a  suitable  position  we  can 
throw  the  rays  they  receive  at  pleasure  on  a  screen.  Thus, 
if  we  mix  together  the  red  and  blue  ray,  a  purple  results ; 
if  the  red  and  yellow,  an  orange ;  and  if  the  yellow  and 
blue,  a  green.  It  is  obvious,  therefore,  that  of  the  colors 
we  have  enumerated  in  Lecture  XL,  as  the  seven  pris- 
matic rays,  the  green,  the  indigo,  and  violet  may  be  com- 
pound, or  secondary  ones,  arising  from  the  intermixture 
of  red,  yellow,  and  blue,  which  by  many  philosophers  are 
looked  upon  as  the  three  primitive  colors. 

We  have  already  remarked  that  there  is  an  analogy  be- 
tween prisms  and  lenses  in  their  action  on  the  rays  of 
light,  and  have  shown  how  rays  become  converging  or  di- 
verging in  their  passage  through  those  transparent  solids. 
In  the  same  manner  it  also  follows,  that  as  prisms  pro- 
duce dispersion  as  well  as  refraction,  so, 
too,  must  lenses:  for,  by  considering 
the  action  of  pairs  of  prisms,  as  in  Fig. 
225,  or  as  we  have  already  done  in  Lec- 
ture XXXIX.,  we  arrive  at  the  action  of 
concave  and  convex  lenses,  and  find  that 
as  refrangibility  differs  for  different  rays 
— being  least  for  the  red  and  most  for 
the  violet — a  lens  acting  unequally  will  cause  objects  to 
be  seen  through  it  fringed  with  prismatic  colors.  This 
phenomenon  passes  under  the  title  of  chromatic  aberra- 
tion of  lenses. 

To  understand  more  clearly  the  nature  of  this,  let  par- 
allel rays  of  red  light  fall  upon  a  plano-convex  lens,  A 

Which  of  the  colors  of  the  spectrum  maybe  regarded  as  compound,  and 
which  as  simple  ?  How  may  it  be  shown  that  lenses  produce  colors  as 
well  as  prisms  I 

I* 


202 


CHROMATIC    ABERRATION. 


B,  Fig.  226,  and  be  converged  by  it  to  a  focus  in  the  point 
r,  the  distance  of  which  from  the  lens  is  measured.   Then 


Fig.  226. 


let  parallel  rays  of  violet  light,  in  like  manner,  fall  on 
the  lens,  and  be  converged  by  it  to  a  focus,  v.  On  being 
measured,  it  will  be  found  that  this  focus  is  much  nearer 
the  lens  than  the  other;  and  the  cause  of  it  is  plainly 
due  to  the  unequal  refrangibility  of  the  two  kinds  of  light. 
The  violet  is  the  more  refrangible,  and  is,  therefore,  more 
powerfully  acted  on  by  the  lens,  and  made  to  converge 
more  rapidly. 

But  this  which  we  have  been  tracing  in  the  case  of  ho- 
mogeneous rays  must  of  course  take  place  in  the  com- 
pound white  light.  On  the  same  principle  that  the  prism 
separates  the  white  light  into  its  constituent  rays  by  act- 
ing unequally  on  them,  so,  too,  will  the  lens.  Parallel 
rays  of  white  light  falling  on  a  lens,  such  as  Fig.  226,  are 
not,  therefore,  converged  to  one  common  focus,  as  repre- 
sented in  Lecture  XXXIX,  but  in  reality  give  rise  to  a 
series  of  foci  of  different  colors,  the  red  being  the  most 
remote  from  the  lens,  and  the  violet  nearest. 

In  some  of  the  most  important  optical  instruments  it  is 
absolutely  necessary  that  this  defect  should  be  avoided, 
and  that  a  method  should  be  hit  upon  by  which  light 
may  be  refracted  without  being  dispersed.  Newton,  who 
believed  that  it  was  impossible  to  succeed  with  this,  gave 
up  the  improvement  of  the  refracting  telescope,  in  which 
it  is  required  that  images  should  be  formed  without  chro- 
matic dispersion,  as  hopeless.  But,  subsequently,  it  was 
shown  that  refraction  without  dispersion  can  be  effected. 
This  is  done  by  employing  two  bodies  having  equal  re- 
fractive, but  unequal  dispersive  powers.  Those  which 

What  is  the  effect  of  a  plano-convex  lens  on  parallel  rays  of  red  and  blue 
light,  respectively  ?  What  is  the  effect  on  white  light  ? 


ACHROMATIC  PRISM  AND  LENS. 


203 


Fig.  227. 


are  commonly  selected  are  crown  and  flint  glass,  which 
refract  nearly  equally.  The  index  for  crown  being  about 
1-53,  and  that  of  flint  T60 ;  but  the  dispersion  of  good 
flint  glass  is  twice  that  of  crown. 

If,  now,  \ve  take  two  prisms,  ABC, 
Fig.  227,  being  of  crown,  and  A  C  D,  of 
flint  glass,  and  place  them,  with  their  bases 
in  opposite  ways,  the  refracting  angle,  C,' 
of  the  latter  being  half  that  of  A,  the 
former,  or,  in  other  words,  adjusted  to 
their  relative  dispersive  powers,  it  will  be  found  that  a  ray 
of  light  passes  through  the  compound  prism,  undergoing  re- 
fraction, and  emerging  without  dispersion;  for  the  incident 
ray,  in  its  passage  through  the  crown  prism  will  be  dis- 
persed into  the  colored  rays,  and  these,  falling  on  the 
flint  prism — the  dispersive  power  of  which  we  assume  to 
be  double,  and  acting  in  the  opposite  direction — will  be  re- 
fracted in  the  opposite  direction,  and  emerge  undispersed. 
Such  an  instrument  is  called  an  achromatic  prism. 

The  same  principle  can,  of  course,  be 
used  in  the  construction  of  lenses,  between 
which  and  prisms  there  is  that  general 
analogy  heretofore  spoken  of.  The  achro- 
matic lens  consists  of  a  concave  lens  of 
flint  and  a  convex  one  of  crown,  the  cur- 
vatures of  each  being  adjusted  on  the  same 
principle  as  the  angles  of  the  achromatic 
prism  are  determined.  Such  an  arrange- 
ment is  represented  in  Fig.  228.  It  gives 
in  its  focus  the  images  of  objects  in 
their  natural  colors,  and  nearly  devoid  of 
fringes. 

But  in  practice,  it  has  been  found  impossible,  by  any 
such  arrangement,  to  effect  the  total  destruction  of  color. 
The  edges  of  luminous  bodies  seen  through  such  lenses 
are  fringed  with  color  to  a  slight  extent.  This  arises 
from  the° circumstance  that  the  dispersive  powers  of  the 
media  employed  are  not  the  same  for  every  colored  ray. 
The  simple  achromatic  lens,  Fig.  228,  will  collect  the  ex- 
How  may  refraction  without  dispersion  be  performed  ?  Describe  the 
structure  of  the  achromatic  prism  ?  What  is  its  mode  of  action  ?  Describe 
the  construction  of  the  achromatic  lens.  Why  are  there  with  these  lenses 
residual  fringes  ? 


204  COLORS    OF    OBJECTS. 

treme  rays  together ;  but  leaves  the  intermediate  ones, 
to  a  small  extent,  outstanding. 

The  theory  of  the  compound  constitution  of  light  ena- 
bles us  to  account,  in  a  clear  manner,  for  the  colors  of 
natural  objects.  Those  which  exhibit  themselves  to  us 
as  white  merely  reflect  back  to  the  eye  the  white  light 
which  falls  on  them,  and  the  black  ones  absorb  all  the  in- 
cident rays.  The  general  reason  of  coloration  is,  there- 
fore, the  absorption  of  one  or  other  tint,  and  the  reflec- 
tion of  the  rest  of  the  spectral  colors.  Thus,  an  object 
looks  blue  because  it  reflects  the  blue  rays  more  copiously 
than  any  others,  absorbing  the  greater  part  of  the  rest. 
And  the  same  explanation  applies  to  red  or  yellow,  and, 
indeed,  to  any  compound  colors,  such  as  orange,  green, 
&c.  That  colored  bodies  do,  in  this  way,  reflect  one  class 
of  rays  more  copiously  than  others  may  be  proved  by 
placing  them  in  the  spectrum.  Thus,  a  red  wafer  seems 
of  a  dusky  tint  in  the  blue  or  violet  regions,  but  of  a  brill- 
iant red  in  the  red  rays. 

On  the  same  principles  we  account  for  the  singular  re- 
sults which  arise  when  monochromatic  lights  fall  on  sur- 
faces of  any  kind.  Thus,  when  spirits  of  wine  is  mixed 
with  salt  in  a  plate,  and  set  on  fire,  the  flame  is  a  mono- 
chromatic yellow — that  is,  a  yellow  unaccompanied  by 
any  other  ray.  If  the  variously  colored  objects  in  a  room 
are  illuminated  with  such  a  light  they  assume  an  extraor- 
dinary appearance  :  the  human  countenance,  for  exam- 
ple, taking  on  a  ghastly  and  death-like  aspect ;  the  red  of 
the  lips  and  the  cheeks  is  no  longer  red,  for  no  red  light 
falls  on  it ;  it  therefore  assumes  a  grayish  tint. 

The  colors  of  transparent  bodies,  such  as  stained  glass 
and  colored  solutions,  arise  from  the  absorption  of  one 
class  of  rays  and  the  transmission  of  the  rest.  Thus, 
there  are  red  glasses  and  red  solutions  which  permit  the 
red  ray  alone  to  traverse  them,  and  totally  extinguish 
every  other.  But,  in  most  cases,  the  colors  of  transpa- 
rent, and  also  of  opaque  bodies,  are  far  from  being  mono- 
chromatic. They  consist,  in  reality,  of  a  great  number 

How  may  the  colors  of  natural  objects  be  accounted  for?  What  is  the 
cause  of  whiteness  and  blackness?  How  can  it  be  proved  that  bodies  re- 
flect some  rays  in  preference  to  others  ?  What  is  monochromatic  light  ? 
What  is  the  cause  of  the  singular  appearance  of  objects  seen  by  such 
lights  ?  What  is  the  cause  of  the  colors  <jf  transparent  bodies  1 


UXDULATORY    THEORY.  205 

of  different  rays.  Thus, common  blue-stained  glass  trans- 
raits  almost  all  the  blue  light  that  falls  upon  it,  and,  in  ad- 
dition, a  little  yellow  and  red. 


LECTURE  XLII. 

UNDULATORY  THEORY  OF  LIGHT. —  Two  Theories  of  Light. 
— Applications  of  the  Corpuscular  Theory. —  Undulatory 
Theory. — Length  of  Waves  is  the  cause  of  Color. — De- 
termination of  Periods  of  Vibration. —  Interference  of 
Light. — Explanations  of  Newton's  Rings,  and  Colors  of 
tJiin  Plates. — Diffraction  of  Light. 

IT  has  been  stated  that  there  are  two  different  theories 
respecting  the  nature  of  light — the  corpuscular  and  the 
undulatory.  In  accounting  for  the  facts  in  relation  to  the 
production  of  colors,  it  is  assumed  that,  in  the  former, 
there  are  various  particles  of  luminous  matter  answering 
to  the  various  colors  of  the  rays,  and  which,  either  alone 
or  by  their  admixture,  give  rise  to  the  different  tints  we 
see.  In  white  light  they  all  exist,  and  are  separated 
from  one  another  by  the  prism,  because  of  an  attractive 
force  which  such  a  transparent  body  exerts ;  and  that  at- 
tractive force  being  unequal  for  the  different  color-giving 
particles,  difference  of  refrangibility  results.  The  colors  of 
natural  objects  on  this  theory  are  explained  by  supposing 
that  some  of  the  col  or- giving  particles  are  reflected  or 
transmitted,  and  others  stifled  or  stopped  by  the  body  on 
which  they  fall.  The  phenomena  of  reflection  by  pol- 
ished surfaces  are  therefore  reduced  to  the  impact  of 
elastic  bodies  ;  and  in  the  same  way  that  a  ball  is  repel- 
led from  a  wall  against  which  it  is  thrown,  so  these  little 
paiticles  are  repelled,  making  their  angle  of  reflexion 
equal  to  their  angle  of  incidence.  But  while  there  are 
many  of  the  phenomena  of  light,  such  as  reflexion,  re- 
fraction, dispersion,  and  coloration,  which  can  be  ac- 
counted for  on  these  principles,  there  are  others  which 

What  are  the  two  theories  of  light  ?  What  is  the  nature  of  the  corpuscu- 
lar theory  ?  On  its  principles  what  is  the  constitution  of  white  light  ?  How 
does  it  account  for  difference  of  refrangibility  and  the  colors  of  natural 
objects  ?  How  does  it  account  for  the  phenomena  of  reflexion  ? 


206  VIBRATIONS  IN  THE  ETHER. 

the  emanation  or  corpuscular  theory  cannot  meet.  These 
are,  however,  explained  in  a  simple  and  beautiful  manner 
by  the  other  theory. 

The  undulatory  theory  rests  upon  the  fact  that  there 
exists  throughout  the  universe  an  elastic  medium  called 
THE  ETHER,  in  which  vibratory  movements  can  be  estab- 
lished very  much  after  the  manner  that  sounds  arise  in 
the  air.  Whatever,  therefore,  has  been  said  in  Lectures 
XXXI,  &c.,  respecting  the  mechanism  and  general  princi- 
ples of  undulatory  movements  applies  here.  Waves  in 
the  ether  are  reflected,  and  made  to  converge  or  di- 
verge on  the  same  principles  that  analogous  results  take 
place  for  waves  upon  water  or  sounds  in  the  air.  It  will 
have  been  observed  already  that  the  reflexions  of  undu- 
lations from  plane,  spherical,  elliptic,  or  parabolic  sur- 
faces, as  given  in  Lecture  XXXII,  are  identically  the 
same  as  those  which  we  have  described  for  light  in  Lec- 
ture XXXVII. 

From  the  phenomena  of  sound  we  can  draw  analogies 
which  illustrate  in  a  beautiful  manner  the  phenomena  of 
light :  for,  as  the  different  notes  of  the  gamut  arise  from 
undulations  of  greater  or  less  frequency,  so  do  the  colors 
of  light  arise  from  similar  modifications  in  the  vibrations 
of  the  ether.  Those  vibrations  that  are  most  rapid  im- 
press our  eyes  with  the  sensation  of  violet,  and  those  that 
are  slower  with  the  sensation  of  red.  The  different  col- 
ors of  light  are,  therefore,  analogous  to  the  different  notes 
of  sound. 

In  Lecture  XXXIII  it  was  shown  how  the  frequency  of 
vibration  which  could  give  rise  to  any  musical  note  might 
be  determined,  and  it  appeared  that  the  ear  could  detect 
vibrations,  as  sound  through  a  range  commencing  with  15 
and  reaching  as  far  as  48,000  in  a  second.  The  frequen- 
cy of  vibration  in  the  ether  required  for  the  production 
of  any  color  has  also  been  determined,  and  the  lengths  of 
the  waves  corresponding.  The  following  table  gives  these 
results.  The  inch  being  supposed  to  be  divided  into  ten 
millions  of  equal  parts,  of  those  parts  the  wave  lengths 


On  what  does  the  undulatory  theory  rest?  Do  the  general  laws  of  undu- 
lations apply  to  the  phenomena  of  light  ?  What  analogy  is  there  be- 
tween sound  and  light  ?  How  do  the  colors  of  light  compare  with  the 
notes  of  sound  ? 


TIMES    OF    VIBRATION.  207 


For  Red        light 
Orange 
yellow 
Green 
Blue 
Indigo 
Violet 


256 
240 
227 
211 
196 
185 
174 


More  recent  investigations  have  proved  the  remarkable 
fact  that  the  length  of  the  most  refrangible  violet  wave 
being  taken  as  one,  that  of  the  least  refrangible  red  will  be 
equal  to  two,  and  the  most  brilliant  part  of  the  yellow 
one  and  a  half. 

Knowing  the  length  of  a  wave  in  the  ether  required  for 
the  production  of  any  particular  color  of  light,  and  the 
rate  of  propagation  through  the  ether,  which  is  195,000 
miles  in  a  second,  we  obtain  the  number  of  vibrations  ex- 
ecuted in  one  second,  by  dividing  the  latter  by  the  former. 

From  this  it  appears  that  if  a  single  second  of  time  be 
divided  into  one  million  of  equal  parts,  a  wave  of  red  light 
vibrates  458  millions  of  times  in  that  short  interval,  and 
a  wave  of  violet  light  727  millions  of  times. 

Further,  whatever  has  been  said  in  Lectures  XXXI 
XXXII,  in  reference  to  the  interference  of  waves,  must 
necessarily,  on  this  theor}',  apply  to  light.  Indeed,  it  was 
the  beautiful  manner  in  which  some  of  the  most  incom- 
prehensible facts  in  optics  were  thus  explained,  that  has 
led  to  its^-almost  universal  adoption  in  modern  times. 
That  light  added  to  light  should  produce  darkness,  seems 
to  be  entirely  beyond  explanation  on  the  corpuscular 
theory ;  but  it  is  as  direct  a  consequence  of  the  undula- 
tory,  as  that  sound  added  to  sound  may  produce  silence. 

From  a  lucid  point,  p,  Fig.  229,  let  rays  of  light  fall 
upon  a  double  prism,  m  n,  the  angle  of  which,  at  C,  is 
very  obtuse.  From  what  has  been  said  respecting  the 
multiplying-glass  (Lecture  XXXVIII),  it  appears  that  an 
eye  applied  at  a  would  see  the  point  p  double,  as  at  p' 
and  p".  Between  these  images  there  is  also  perceived  a 
number  of  bright  and  dark  lines  perpendicular  to  a  line 
joining  p'  and  p".  On  covering  one  half  the  prism  the 
lines  disappear,  and  only  one  image  is  seen. 

What  relation  of  wave  length  exists  between  the  least,  the  intermediate, 
and  the  most  refrangible  rays?  How  may  the  frequency  of  vibrations  be 
determined  from  the  wave  length  ?  What  is  that  frequency  in  the  case  of 
red  and 'violet  light?  Does  interference  of  luminous  waves  take  place? 
How  is  this  exhibited  by  the  double  prism,  Fig.  229  ? 


208 


INTERFERENCE    OF    LIGHT. 


This  alternation  of  light  and  darkness  is  caused  by 
ethereal  waves  from  the  points  p'  and^?"  crossing  one  an- 
other, and  giving  rise  to  interference.  If,  therefore,  with 

Fig.  229. 


those  points  as  centers,  we  draw  circular  arcs,  0,  1,  2, 
3,  4,  &c.,  these  may  represent  waves,  the  alternate  lines 
between  them  being  half  waves.  It  will  be  perceived 
that  wherever  two  whole  waves  or  two  half  waves  en- 
counter, they  mutually  increase  each  other's  effect  ;  but 
if  the  intersection  takes  place  at  points  where  the  vibra- 
tions are  in  opposite  directions,  interference,  and,  there- 
fore, a  total  absence  of  light  results,  as  is  marked  in  the 
figure  by  the  large  dots. 

Wherever,  therefore,  rays  of  light  are  arranged  so 
as  to  encounter  one  another  in  opposite  phases  of  vi- 
bration, interference  takes  place.  Thus,  if  we  take  a 
230  convex  lens,  of  very  long  focus,  and 

press  it  upon  a  flat  glass  by  means  of 
screws,  Fig.  230,  at  the  point  of  con- 
tact, when  we  inspect  the  instrument 
by  reflected  light  a  black  spot  will  be 
seen,  surrounded  alternately  by  light 
i<-er  and  dark  rings.  These  pass  under  the 
name  of  Newton's  colored  rings.  When  the  light  is  ho- 
mogeneous the  dark  rings  are  black,  and  the  colored  ones 
of  the  tint  which  is  employed,  but  when  it  is  common 


What  is  the  effect  of  two  whole  or  two  half  waves  encountering? 
When  does  interference  take  place?  Describe  the  process  for  forming 
Newton's  colored  rings. 


DIFFRACTION    OF    LIGHT.  209 

white  light  the  central  black  spot  is  surrounded  by  a  se- 
ries of  colors.  When  the  instrument  is  inspected  by 
transmitted  light,  the  colors  are  all  complementary,  and 
the  central  spot  is  of  course  white.  These  rings  arise 
from  the  interference  of  the  rays  reflected  from  the  ante- 
rior and  posterior  boundaries  between  the  two  glasses. 
The  colors  of  soap-bubbles  and  thin  plates  of  gypsum, 
are  referable  to  the  same  cause. 

By  the  diffraction  of  light  is  meant  its  deviation  from 
the  rectilinear  path,  as  it  passes  by  the  edges  of  bodies  or 
Fig.  231.  through  apertures.     It  arises  from 

the  circumstance  that  when  ethereal, 
or,  indeed,  any  kind  of  waves  im- 
pinge on  a  solid  body,  they  give  rise 
to  new  undulations,  originating  at  the 
place  of  impact,  and  often  producing 
interference.  Thus,  if  a  diverging 
beam  of  light  passes  through  an  ap- 
erture, a  b,  Fig.  231,  in  a  plate  of 
metal  an  eye  placed  beyond  will  dis- 
cover a  series  of  light  and  dark  fringes.  The  cause  of 
these  has  been  already  explained  in  Lecture  XXXII.,  in 
which  it  was  shown  that  from  the  points  a  and  b  new 
systems  of  undulations  arise,  which  interfere  with  one  an- 
other, and  also  with  the  original  waves. 

What  is  the  cause  of  them  ?  What  is  the  cause  of  the  colors  of  soap- 
bubbles  and  their  films  generally  ?  What  is  meant  by  the  diffraction  of 
light? 


f 


210  POLARIZATION    OF    LIGHT. 


LECTURE  LXIII. 

OF  POLARIZED  LIGHT. — Peculiarity  of  Polarized  Light. — 
Illustrated  by  the  Tourmaline. — Polarization  by  Reflex- 
ion.— General  Law  of  Polarization. — Positions  of  no 
Reflexion. — Plane  of  Polarization. — Polarization  by 
Refraction. — Application  of  the  Undulatory  Theory. — 
The  Polariscopc. 

WHEN  a  ray  of  common  light  is  allowed  to  fall  on  the 
surface  of  a  piece  of  glass  it  can  be  equally  reflected  by 
the  glass  upward,  downward,  or  laterally. 

If  such  a  ray  falls  upon  a  glass  plate  at  an  angle  of 
56°,  and  is  received  upon  a  second  similar  plate  at  a  sim- 
ilar angle,  it  will  be  found  to  have  obtained  new  proper- 
ties :  in  some  positions  it  ca.n  be  reflected  as  before,  in 
others  it  cannot.  On  examination,  it  is  discovered  that 
these  positions  are  at  right  angles  to  one  another. 

Again :  if  a  ray  of  light  be  caused  to  pass  through  a 
Fig.  232.  plate  of  tourmaline,  c  d,  Fig. 

C/AM^e  A,  232>  m  tne  direction  a  b,  and 
be  received  upon  a  second  plate, 
'  placed  symmetrically  with  the 
first,  it  passes  through  both  with- 
out difficulty.  But  if  the  second 
plate  be  turned  a  quarter  round,  as  at  g  h,  the  light  is 
totally  cut  off. 

Considering  these  results,  it  therefore  appears  that  we 
can  impress  upon  a  ray  of  light  new  properties  by  cer- 
tain processes,  and  that  the  peculiarity  consists  in  giving 
it  different  properties  on  different  sides.  Such  a  ray, 
therefore,  is  spoken  of  as  a  ray  of  polarized  light. 

When  light  is  polarized  by  reflexion,  the  effect  is  only 
completely  produced  at  a  certain  angle  of  incidence, 
which  therefore  passes  under  the  name  of  the  angle  of 

What  is  observed  in  the  reflexion  of  ordinary  light  ?  What  occurs 
when  light  which  has  already  been  reflected  at  56°  is  attempted  to  be  re- 
flected again?  Describe  the  action  of  a  tourmaline.  What  is  meant  by 
polarized  light?  Under  what  circumstances  does  maximum  polarization 
take  place  ' 


POLARIZATION    OF    LIGHT. 


211 


maximum  polarization.   It  takes  place  when  the  reflected 
ray  makes,   with    the    refracted   ray,  an  angle    of  90°. 

Fig.  233. 


Thus,  let  A  B,  Fig.  233,  be  a  plate  of  glass,  a  b  an  inci- 
dent ray,  which,  at  b,  is  partly  reflected  along  b  c  and 
partly  refracted  along  b  e,  emerging  therefrom  at  e  d. 
Now,  maximum  polarization  ensues  when  c  b  e  is  a 
right  angle,  from  which  it  follows  that  the  polarizing 
power  is  connected  with  the  refractive,  the  law  being 
that  "  the  index  of  refraction  is  the  tangent  of  the  angle 
of  polarization." 

Let  A  B,  Fig.  234,  be  a  plate  of  glass,  on  which  a 
ray  of  light,  a  b, 
falls,  and  after  po- 
larization is  reflect- 
ed along  be;  ate  let 
it  be  received  on  a 
second  plate,  C  D, 
similar  to  the  for- 
mer, and  capable 
of  revolving  on  c  b, 
as  it  were  on  an 
axis.  Let  us  now 
examine  in  what 
positions  of  this 
plate  the  polaiized  ray,  b  c,  can  be  reflected,  and  in  what 
it  cannot. 


What  is  the  law  connecting  refraction  and  polarization?  What  are  the 
relative  positions  of  the  reflecting  plates  when  the  ray  cannot  be  re- 
flected? 


212  PHENOMENA    OF    POLARIZATION. 

Experiment  at  once  shows  that  when  the  plane  of  re- 
flexion of  the  first  mirror  coincides  with  the  plane  of  rc- 
2^.235.  flexion  of  the  second, 

the  polarized  ray  un- 
dergoes reflexion  ; — 
but  if  they  are  at  right 
angles  to  one  another, 
it  is  no  longer  reflect- 
ed.  To  make  this 
clear,  let  a  b,Fig.  235, 
be  the  first  mirror,  and 
c  d  the  second,  so  ar- 
ranged as  to  present 
their  edges,  as  seen 
depicted  on  this  page. 
Again  :  let  cf  be  the 
first  and  g  li  the  sec- 

i 1.   ond,  now  turned  half 

•*? —  way  round,  but  still 
presenting  its  edge,  in 
both  those  positions, 
the  planes  of  incidence 

j |0  and  reflexion  of  both 

the  mirrors  coincid- 
ing, the  ray  polarized 

by  a  b  or  ef  will  be  reflected.  But  if,  as  in  i  &,  the  sec- 
ond mirror,  I,  is  turned  so  as  to  present  its  face,  or,  as 
in  m  n,  it  is  turned  at  o,  so  as  to  present  its  back,  in 
these  cases,  the  planes  of  incidence  and  reflexion  of  the 
two  mirrors  being  at  right  angles,  the  polarized  ray  can 
no  longer  be  reflected.  We  have,  therefore,  two  posi- 
tions in  which  reflexion  is  possible,  and  two  in  which  it 
is  impossible,  and  these  are  at  right  angles  to  one 
another.  By  the  plane  of  polarization  we  mean  the  plane 
in  which  the  ray  can  be  completely  reflected  from  the 
second  mirror. 

When  a  ray  of  light  falls  on  the  surface  of  a  transparent 
medium,  it  is  divided  into  two  portions,  as  has  already 
been  said,  one  of  tflese  being  reflected  and  the  other  re- 
fracted. On  examination,  both  these  rays  are  found  to 
be  polarized,  but  they  are  polarized  in  opposite  ways,  or 

What  is  the  plane  of  polarization  1  In  the  case  of  a  transparent  me- 
dium, what  is  the  relation  between  the  reflected  and  refracted  rays  1 


EXPLANATION    OF    POLARIZATION.  213 

rather  the  plane  of  polarization  of  the  refracted  is  at 
right  angles  to  the  plane  of  polarization  of  the  reflect- 
ed ray. 

When  it  is  required  to  polarize  light  by  refraction  a 
pile  of  several  plates  of  thin  glass  is  used,  for  polarization 
from  a  single  surface  is  incomplete. 

On  the  undulatory  theory  we  can  give  a  very  clear 
account  of  all  these  phenomena.  Common  light  origi- 
nates in  vibratory  movements  taking  place  in  the  ether  ; 
but  it  differs  from  the  vibrations  in  the  air  which  consti- 
tute sound  in  this  essential  particular  that,  while  in  the 
waves  of  sound  the  movements  of  the  vibrating  particles 
lie  in  the  course  of  the  ray,  in  the  case  of  light  they  are 
transverse  to  it.  This  may  be  made  plain  by  considering 
the  wave-like  motions  into  which  a  cord  may  be  thrown 
by  shaking  it  at  one  end,  the  movement  being  in  the 
up-and-down  or  in  the  lateral  direction,  while  the  wave 
runs  straight  onward.  The  ethereal  particles,  therefore, 
vibrate  transversely  to  the  course  of  the  ray.  But  then 
there  are  an  infinite  number  of  directions  in  which  these 
transverse  vibrations  may  be  made  :  a  cord  may  be  shaken 
vertically  or  laterally,  or  in  an  infinite  number  of  inter- 
mediate angular  positions,  all  of  which  are  transverse  to 
its  length. 

Common  light,  therefore,  arises  in  ethereal  vibrations, 
taking  place  in  every  possible  direction  transverse  to  the 
path  of  the  ray ;  but  in  polarized  light  the  vibrations  are 
all  in  one  plane.  Thus,  in  the  case  of  the  tourmaline, 
when  a  ray  passes  through  it  all  the  vibrations  are  taking 
place  in  one  direction,  and  therefore  the  ray  can  pass 
through  a  second  plate  placed  symmetrically  with  the 
first ;  but  if  the  second  be  turned  a 
quarter  round  the  vibrations  can  no 
longer  pass,  just  in  the  same  way  th 
a  sheet  of  paper,  c  d,  may  be  slipped 
through  a  grating,  a  b,  while  its  plane 
coincides  with  the  length  of  the  bars; 
but  can  no  longer  go  through  when  it  is 
turned  as  at  ef,  a  quarter  round. 

How  is  light  to  be  polarized  by  refraction  ?  What  is  light  according  to 
the  undulatory  theory?  In  what  directions  are  the  vibrations  made? 
How  may  this  be  illustrated  by  a  cord?  In  what  directions  are  the  vibra- 
tions of  polarized  light  ?  How  is  this  illustrated  ia  Fig.  236  ? 


214 


POLARIZED    RAYS. 


Fig.  237. 


Again,  in  the  case  of  polarization  by  reflexion,  let  A  B, 

Fig.  237,  be  the  mirror  on 
which  a  ray  of  common 
light,  a  b,  falls  at  the  prop- 
er angle  of  polarization, 
and  is  reflected  in  a  polar- 
ized condition  along  b  c. 
C  D  will  be  the  plane  in 
which  the  ethereal  parti- 
cles vibrate  after  reflection, 
and  the  curve  line  drawn 
on  it  may  represent  .the 
intensities  of  their  vibra- 
tions. 

So,  too,  in  Fig.  238,  we 
have  an  illustration  of  polarization  by  refraction.    Let  A  B 


Fig  238. 


be  a  bundle  of  glass  plates, 
a  b  the  incident,  and  c  d  the 
polarized  ray;  the  plane  C  D 
at  right  angles  to  the  plates 
is  the  plane  of  polarization, 
and  the  curve  drawn  on  it 
represents  the  intensities 
with  which  the  polarized 
particles  move. 

In  every  instance  the  plane 
of  polarization  is  perpendic- 


ular to  the  planes  of  reflexion  and  refraction. 

Fig.  239.  The  polariscope  is  an  instru- 

ment for  exhibiting  the  proper- 
ties of  polarized  light.  There 
are  many  different  forms  of  it  : 
Fig.  239  represents  one  of 
them.  It  consists  of  a  mirror 
of  black  glass,  a,  which  can  be 
set  at  any  suitable  angle  to  the 
brass  tube,  A  B,  by  means  of  a 
graduated  arc,  e;  it  can  also  be 
rotated  on  the  axis  of  the  tube 

B  A,  and  the  amount  of  that  rotation  read  off  on  the 

What  is  the  illustration  given  as  respects  reflected  light  in  Fig.  237  ? 
What  is  it  for  refracted  light  in  Fig.  238  ?  What  is  the  constant  position 
of  the  plane  of  polarization  ?  Describe  the  polariscope. 


DOUBLE    REFRACTION.  215 

graduated  circle  b.  At  the  other  end  of  the  tube  there 
is  a  second  mirror  of  black  glass,  d,  which,  like  a,  can  be 
arranged  at  any  required  angle,  and  likewise  turned 
round  on  the  axis  of  the  brass  tube,  A  B,  the  amount  of 
its  rotation  being  ascertained  by  the  divided  circle,  c. 
Sometimes  instead  of  this  mirror  of  black  glass,  a  bundle 
of  glass  plates  in  a  suitable  frame  is  useo!.  The  instru- 
ment is  supported  on  a  pillar,  C. 

The  fundamental  property  of  light  polarized  by  re- 
flexion may  be  exhibited  by  this  instrument  as  follows  : — 
Set  its  two  mirrors,  a  and  d,  so  as  to  receive  the  light 
which  falls  on  them  at  an  angle  of  56°.  Then,  when  the 
first,  a,  makes  its  reflexion  in  a  vertical  plane,  the  light 
can  be  reflected  by  d  also  in  a  vertical  plane,  upward  or 
downward.  But  if  d  be  turned  round  90°,  so  as  to 
attempt  to  reflect  the  ray  to  the  right  or  left  in  a  hori- 
zontal plane,  it  will  be  found  to  be  impossible,  the  light 
becoming  extinct  and  in  intermediate  positions;  as  the 
mirror  revolves  the  light  is  of  intermediate  intensity. 


LECTURE  XLIV. 

ON  DOUBLE  REFRACTION  AND  THE  PRODUCTION  OP  COL- 
ORS IN  POLARIZED  LIGHT. — Double  Refraction  of  Ice- 
land Spar. — Axis  of  the  Crystal. — Crystals  with  two 
Axes.  —  Production  of  Colors  in  Polarized  Light. — 
Complementary  Colors  Produced. —  Colors  Depend  071 
the  Thickness  of  the  Film. — Symmetrical  Rings  and 
Crosses. — Colors  Produced  by  Heat  and  Pressure. — 
Circular  and  Elliptical  Polarization. 

BY  double  refraction  we  mean  a  property  possessed  by 
certain  crystals,  such  as  Iceland  spar,  of  dividing  a  single 
incident  ray  into  two  emergent  ones.  Thus,  let  R  r  be  a 
ray  of  light  falling  on  a  rhomboid  of  Iceland  spar,  ABC 
X,  in  the  point  r,  it  will  be  divided  during  its  passage 
through  the  crystals  into  two  rays,  r  E,  r  O,  the  latter  of 

How  may  this  instrument  be  used  to  exhibit  light  polarized  by  reflexion  ? 
What  is  meant  by  double  refraction?  Describe  the  phenomena  exhibited 
by  a  crystal  of  Iceland  spar. 


216 


DOUBLE    REFRACTION. 


Fig.  240. 


-.N 


Fig.  241. 


which  follows  the  ordi- 
n  nary  law  of  refraction, 
and  therefore  takes  the 
name  of  the  ordinary  ray, 
the  former  follows  a  dif- 
ferent law  and  is  spoke 
of  as  the  extraordinary 
ray. 

Through  such  a  crys- 
tal objects  appear  double. 
A  line,  M  N,  on  a  piece  of 
paper  viewed  through  it  is  exhibited  as  two  lines,  M  N,m 
n,  the  amount  of  separation  depending  on  the  thickness 
of  the  crystal.  The  emergent  rays  E  e,  O  o,  are  parallel 
after  they  leave  the  surface  X. 

A  line  drawn  through  the  crystal  from 
one  of  its  obtuse  angles  to  the  other  is 
called  the  axis  of  the  crystal,  and  if  arti- 
ficial planes  be  ground  and  polished  as 
n  m,  op,  perpendicular  to  this  axis,  a  b, 
Fig.  241,  rays  of  light  falling  upon  this 
axis  or  parallel  to  it  do  not  undergo 
double  refraction. 

Fig.  242.  Or,  if  new  faces,  o  p,  n  m,  Fig.  242, 

•I  be  ground  and  polished  parallel  to  the 
axis  a  b,  a  ray  falling  in  the  direction  df 
also  remains  single. 

But  if  the  refracting  faces  are  neither 
at  right  angles  nor  parallel  to  the  axis, 
double  refraction  always  ensues. 
While  Iceland  spar  has  only  one  axis  of  double  refrac- 
tion, there  are  other  crystals,  such  as  mica,  topaz,  gypsum, 
&c.,  that  have  two.  In  crystals  that  have  but  one  axis 
there  are  differences.  In  some  the  extraordinary  ray  is 
inclined  from  the  axis  in  others  toward  it  when  compared 
with  the  ordinary  ray.  The  former  are  called  negative 
crystals,  the  latter  positive. 

The  explanation  which  the  undulatory  theory  gives  of 
this  phenomenon  in  crystals  having  a  principal  axis  is, 
that  the  ether  existing  in  the  crystal  is  not  equally  elastic 

What  is  the  axis  of  the  crystal  ?  In  what  cases  does  an  incident  ray  not 
undergo  double  refraction  ?  What  crystals  have  two  axes  of  double  refrac- 
tion ?  What  are  negative  crystals  ?  What  are  positive  ones  ? 


ff, 


COLORS    IN    POLARIZED    LIGHT. 


217 


in  every  direction.  Undulations  are  therefore  propagated 
unequally,  and  a  division  of  the  ray  takes  place,  those 
undulations  which  move  quickest  having  the  less  index  of 
refraction. 

When  the  two  rays  emerging  from  a  rhomb  of  Iceland 
spar  are  examined,  they  afe  both  found  to  consist  of  light 
totally  polarized,  the  one  being  polarized  at  right  angles 
to  the  other. 

We  have,  therefore,  several  different  ways  in  which 
light  can  be  polarized — by  reflexion,  refraction,  absorp- 
tion, and  double  refraction. 

When  a  crystal  of  Iceland  spar  is  ground  to  a  prismatic 
shape,  and  then  achromatized  by  a  prism  of  glass,  it  forms 
one  of  the  most  valuable  pieces  of  polarizing  apparatus 
that  we  have.  Such  a  prism  may  be  used  to  very  great 
advantage  instead  of  the  mirror  of  the  apparatus,  Fig.  239. 

If  a  ray  of  polarized  light  is  passed  through  a  thin 
plate  of  certain  crystalized  bodies,  such  as  mica  or  gyp- 
sum, and  the  light  then  viewed  through  an  achromatic 
prism  or  by  reflexion  from  the  second  mirror  of  the 
polarizing  machine,  Fig.  239,  brilliant  colors  are  at  once 

Fig.  243. 


developed.  Thus,  let  R  A  be  a  ray  of  light  incident  on 
the  first  mirror  of  the  polariscope,  A  G  the  resulting 
polarized  ray,  and  D  E  F  G  be  a  thin  plate  of  gypsum 
or  mica.  If,  previous  to  the  introduction  of  this  plate, 
the  two  mirrors  A  and  C  be  crossed,  or  at  right  angles  to 
one  another,  the  eye  placed  at  E  will  perceive  no  light ; 

What  is  the  explanation  of  double  refraction  on  the  undulatory  theory? 
\Vhat  is  the  condition  of  the  emergent  rays?  In  what  ways  may  light 
be  polarized  ?  Under  what  circumstances  are  colors  developed  by  polar- 
ized light  ? 


218  COLORS   IN    POLARIZED    LIGHT. 

but,  on  the  introduction  of  the  crystal,  its  surface  appears 
to  be  covered  with  brilliant  colors,  which  change  their 
tints  according  as  it  is  inclined,  or  as  the  light  passes 
through  thicker  or  thinner  places.  On  further  examination 
it  will  be  found  that  there  are  two  lines,  D  E  and  F  G, 
which,  when  either  of  them  is  parallel  or  perpendicular 
to  the  plane  of  polarization,  R  A  C  or  A  C  E,  no  colors 
are  produced.  But  if  the  plate  be  turned  round  in  its 
own  plane  a  single  color  appears,  which  becomes  most 
brilliant  when  either  of  the  lines  a  b,  c  d,  inclined  45°,  to 
the  former  ones  are  brought  into  the  plane  of  polarization. 
The  former  lines  are  called  the  neutral,  and  the  latter  the 
depolarizing  axes  of  the  film. 

This  is  what  takes  place  so  long  as  we  suppose  the  two 
mirrors,  A  C,  fixed ;  but  if  we  make  the  mirror  nearest 
to  the  eye  revolve  while  the  film  is  stationary,  the  phe- 
nomena are  different.  Let  the  film  be  of  such  a  thickness 
as  to  give  a  red  tint,  and  be  fixed  in  such  a  position  as 
to  give  its  maximum  coloration,  and  the  eye-mirror  to  re- 
volve, it  will  be  found  that  the  brilliancy  of  the  color  de- 
clines, and  it  disappears  when  a  revolution  of  45°  has 
been  accomplished ;  and  now  a  pale  green  appears,  which 
increases  in  brilliancy  until  90°  are  reached,  when  it  is  at 
a  maximum.  Still  continuing  the  revolution,  it  becomes 
paler,  and  at  135°  it  has  ceased,  and  a  red  blush  com- 
mences, which  reaches  its  maximum  at  180°  ;  and  the 
same  system  of  changes  is  run  through  in  passing  from 
180°  to  360°  ;  so  that  while  the  film  revolves  only  one 
color  is  seen,  but  as  the  mirror  revolves  two  appear, 
If,  instead  of  using  a  mirror,  we  use  an  achromatic 
Fig.  244.  prism,  we  have  two  im- 

ages of  the  film  at  the 
same  time,  and  we  find 
that  they  exhibit  comple- 
mentary colors — that  is, 
colors  of  such  a  tint  that 
if  they  be  mixed  togeth- 
er they  produce  white 
light.  This  effect  is  rep- 
resented in  Fig.  244. 

What  are  the  neutral  axes  of  the  film?  What  are  its  depolarizing  axes  ? 
what  takes  place  when  the  film  is  stationary  and  the  mirror  revolves  ? 
What  is  the  relation  of  the  two  resulting  colors  to  each  other? 


RINGS    AND   CROSSES. 


219 


That  the  particular  colors  which  appear  depend  on  the 
thickness  of  the  films,  is  readily  established  by  taking  a 
thin  wedge-shaped  piece  of  sulphate  of  lime,  and  expos- 
ing it  in  the  polariscope ;  all  the  different  colors  are  then 
seen,  arranged  in  stripes  according  to  the  thickness  of  the 
film. 

When  a  slice  of  an  uniaxial  crystal  cut  at  right  angles 
to  the  axis  is  used  instead  of  the  films,  in  the  foregoing 
experiment,  very  brilliant  effects  are  produced,  consisting 

Fig.  245. 


of  a  series  of  colored  rings,  arranged  symmetrically  and 
marked  in  the  middle  by  a  cross,  which  may  either  be  light 
or  dark — light  if  the  second  mirror  is  in  the  proper  po- 
sition to  reflect  the  light  from  the  first,  and  dark  if  it  be 
at  right  angles  thereto. 

In  crystals  having  two  axes  a  complicated  system  of 
oval  rings,  originating  round  each  axis,  may  be  perceiv- 

Fig.  246. 


ed,  intersected  by  a  cross.  Fig.  246,  represents  the  ap- 
pearance in  a  crystal  of  nitrate  of  potash  ;  and  in  the  same 
way  other  figures  arise  with  different  crystals. 

How  can  it  be  proved  that  the  color  is  determined  by  the  thickness  of 
the  film?  What  phenomena  are  seen  when  slices  from  crystals  are  used  ? 
With  crystals  of  two  axes  what  are  the  results  ? 


220  EFFECTS    OF    PRESSURE,    ETC. 

If  transparent  noncrystalized  bodies  are  employed  in 
these   experiments,   no  colors   whatever  are  perceived. 

Fig.  247. 


Thus,  a  plate  of  glass  placed  in  the  polariscope,  gives 
rise  to  no  such  development ;  but  if  the  structure  of  the 
glass  be  disturbed,  either  by  warming  it  or  cooling  it  un- 
equally, or  if  it  be  subjected  to  unequal  pressure  from 
screws,  then  colors  are  at  once  developed.  This  proper- 
ty may,  however,  be  rendered  permanent  in  glass,  by  heat- 
ing it  until  it  becomes  soft  and  then  cooling  it  with  rap- 
idity. 

All  the  phenomena  here  described  belong  to  the  divi- 
sion of  plane  polarization — but  there  are  other  modifica- 
tions which  can  be  impressed  on  light,  giving  rise  to  very 
remarkable  and  intricate  results  :  these  are  designated 
circular,  elliptical,  &c.,  polarization.  The  mechanism  of 
the  motions  impressed  on  the  ether  to  produce  these  re- 
sults is  not  difficult  to  comprehend  ;  for  common  light,  as 
has  been  stated,  originates  in  vibrations  taking  place  in 
every  direction  transverse  to  the  ray;  plane  polarized  light 
arises  from  vibrations  in  one  direction  only  :  and  when  the 
ethereal  molecules  move  in  circles  they  originate  circular- 
ly polarized  light,  and  if  in  ellipses,  elliptical. 

When  glass  is  unequally  warmed  or  cooled,  or  subjected  to  unequal 
pressure*,  what  is  the  result  ?  How  may  these  effects  be  made  perma- 
nent? What  modification  of  the  ether  gives  rise  to  plane  polarization  ? 
What  to  circular  and  what  to  elliptical  ? 


THE    KAINBOW.  221 


LECTURE  XLV. 

NATURAL  OPTICAL  PHENOMENA. —  The  Rainbow. — Condi- 
tions of  its  Appearance. — Formation  of  the  Inner  Bow. 
— Formation  of  the  Outer  Bow. —  The  Bows  are  Cir- 
cular Arcs.  —  Astronomical  Refraction.  —  Elevation  of 
Objects.—  The  Ticilight. — Reflexion  from  the  Air. — Mi- 
rages and  Spectral  Apparitions,  and  Unusual  Refraction. 

THE  rainbow,  the  moat  beautiful  of  meteorological 
phenomena,  consists  of  one  or  more  circular  arcs  of  pris- 
matic colors,  seen  when  the  back  of  the  observer  is  turn- 
ed to  the  sun,  and  rain  is  falling  between  him  and  a  cloud, 
which  serves  as  a  screen  on  which  the  bow  is  depicted. 
When  two  arches  are  visible  the  inner  one  is  the  most 
brilliant,  and  the  order  of  its  colors  is  the  same  in  which 
they  appear  in  the  prismatic  spectrum — the  red  fringing 
its  outer  boundary,  and  the  violet  being  within.  This 
is  called  the  primary  bow.  The  secondary  bow,  which  is 
the  outer  one,  is  fainter,  and  the  colors  are  in  the  invert- 
ed order.  When  the  sun's  altitude  above  the  horizon  ex- 
ceeds 42°  the  inner  bow  is  not  seen,  and  when  it  is  more 
than  54°  the  outer  is  invisible.  If  the  sun  is  in  the  hori- 
zon, both  bows  are  semicircles,  and  according  as  his  alti- 
tude is  greater  a  less  and  less  portion  of  the  semicircle  is 
visible  ;  but  from  the  top  of  a  F-  343 

mountain  bows  that  are  larger 
than  a  semicircle  may  be  seen. 

These  prismatic  colors  arise 
from  reflexion  and  refraction 
of  light  by  the  drops  of  rain, 
which  are  of  a  spherical  figure. 
In  the  primary  bow  there  is 
one  reflexion  and  two  refrac- 
tions ;  in  the  secondary  there 

Under  what  circumstances  does  the  rainbow  form?  Of  the  two  bows 
which  is  the  most  brilliant  ?  What  is  the  order  of  the  colors  ?  What  is 
their  order  in  the  secondary  bow  ?  What  are  the  circumstances  which  de- 
termine the  visibility  of  each  bow  ?  When  are  they  semicircles  ?  When 
more  than  semicircles  ?  How  is  the  primary  bow  formed  ? 


222  THE    RAINBOW. 

are  two  reflexions  and  two  refractions.  Thus,  let  S,  Fig. 
248,  be  a  ray  of  light,  incident  on  a  raindrop,  a  ;  on  ac- 
count of  its  obliquity  to  the  surface  of  the  drop,  it  will  be 
refracted  into  a  new  path,  and  at  the  back  of  the  drop  it 
will  undergo  reflexion,  and  returning  to  the  anterior  face 
and  escaping  it  will  be  again  refracted,  giving  rise  to 
violet  and  red  and  the  intermediate  prismatic  colors 
between,  constituting  a  complete  spectrum;  and  as  the 
drops  of  rain  are  innumerable  the  observer  will  see  in- 
numerable spectra  arranged  together  so  as  to  form  a  cir- 
cular arc. 

m    ^g  The  secondary  rainbow  arises 

"  from  two  refractions  and  two  re- 
flexions of  the  rays.  Thus,  let 
the  ray  S,  Fig.  249,  enter  at  the 
bottom  of  the  drop,  it  passes  in 
the  direction  toward  I'  after  hav- 
ing undergone  refraction  at  the 
front;  from  I'  it  moves  to  I",  where 
it  is  a  second  time  reflected,  and  then  emerges  in  front, 
undergoing  refraction  and  dispersion  again.  For  the 
same  reason  as  in  the  other  case,  prismatic  spectra  are 
seen  arranged  together  in  a  circular  arc  and  form  a  bow. 
In  Fig.  250,  let  O  be  the  spectator  and  O  P  a  line 
drawn  from  his  eye  to  the  center  of  the  bows.  Then 
rays  of  the  sun,  S  S,  falling  on  the  drops  ABC,  will 
produce  the  inner  bow,  and  falling  on  D  E  F,  the  outer 
bow,  the  former  by  one  and  the  latter  by  two  reflexions. 
The  drop  A  reflects  the  red,  B  the  yellow,  and  C  the  blue 
rays  to  the  eye ;  and  in  the  case  of  the  outer  bow,  F  the 
red,  E  the  yellow,  and  D  the  blue.  And  as  the  color 
perceived  is  entirely  dependent  on  the  angle  under  which 
the  ray  enters  the  eye,  as  in  the  case  of  the  interior  bow, 
the  blue  entering  at  the  angle  COP,  the  yellow  at  the 
larger  angle  BOP,  and  the  red  and  the  largest  A  O  P, 
we  see  the  cause  why  the  bows  are  circular  arcs.  For 
out  of  the  innumerable  drops  of  rain  which  compose  the 
shower,  those  only  can  reflect  to  the  eye  a  red  color 
which  make  the  same  angle,  A  O  P,  that  A  does  with 
the  line  O  P,  and  these  must  necessarily  be  arranged  in 

What  are  the  conditions  for  the  formation  of  the  secondary  bow  ?    Why 
are  both  bows  circular  arcs  ? 


THE    RAINBOW. 


223 


a  circle  of  which  the  center  is  P.     And  the  same  reason- 
ing applies  for  the  yellow,  the  blue,  or  any  other  ray  as 


well  as  the  red,  and  also  for  the  outer  as  well  as  the  inner 
bow. 

*  Another  interesting  natural  phenomenon  connected 
with  the  refraction  of  light  is  what  is  called  "  astronomi- 
cal refraction,"  arising  from  the  action  of  the  atmosphere 
on  the  rays  of  light.  It  is  this  which  so  powerfully  dis- 
turbs the  positions  of  the  heavenly  bodies,  making  them 
appear  higher  above  the  horizon  than  they  really  are, 
and  changes  the  circular  form  of  the  sun  and  moon 
to  an  oval  shape.  It  also  aids  in  giving  rise  to  the  twi- 
light. 

Let  O  be  the  position  of  an  observer  on  the  earth,  Z, 

What  is  the  cause  of  astronomical  refraction  ? 


224 


ASTRONOMICAL  REFRACTION. 


Fig.  251,  will  be  his  zenith,  and  let  R  be  any  star,  the  rays 
from  which  come,  of  course,  in  straight  lines,  such  as  R 
E.  Now,  when  such  a  ray  impinges  on  the  atmosphere 
Fig.  251.  at  s,  it  is  refracted,  and 

deviates  from  its  recti- 
linear course.  At  first 
this  refraction  is  fee- 
ble, but  the  atmos- 
phere continually  in- 
creases in  density  as 
we  descend  in  it,  and 
therefore  the  deviation 
c  of  the  ray  from  its  orig- 
inal path,  R  E,  be- 
comes continually  greater.  It  follows  a  curvilinear  line, 
and  finally  enters  the  eye  of  the  observer  at  O.  This  may 
perhaps  be  more  clearly  understood  by  supposing  the 
concentric  circles,  a  a,  b  b,  c  c,  represented  in  the  figure, 
to  stand  for  concentric  shells  of  air  of  the  same  density, 
the  ray  at  its  entry  on  the  first  becomes  refracted,  and 
pursues  a  new  course  tx>  the  second.  Here  the  same 
thing  again  takes  place,  and  so  with  the  third  and  other 
ones  successively.  But  these  abrupt  changes  do  not  oc- 
cur in  the  atmosphere,  which  does  not  change  its  density 
from  stratum  to  stratum  abruptly,  but  gradually  and  con- 
tinually. The  resulting  path  of  the  ray  is,  therefore,  not 
a  broken  line,  but  a  continuous  curve. 

Now,  it  is  a  law  of  vision  that  the  mind  judges  of  the 
position  of  an  object  as  being  in  the  direction  in  which 
the  ray  by  which  it  is  seen  enters  the  eye.  Consequently 
the  star,  R,  which  emits  the  ray  we  have  under  consider- 
ation, will  be  seen  in-  the  direction,  Or — that  being  the 
direction  in  which  the  ray  entered  the  eye — and,  there- 
fore, the  effect  of  astronomical  refraction  is  to  elevate  a 
star  or  other  object  above  the  horizon  to  a  higher  appa- 
rent position  than  that  which  it  actually  occupies. 

Astronomical  refraction  is  greater  according  as  the  ob- 
ject is  nearer  the  horizon,  becoming  less  as  the  altitude 


Trace  the  path  of  a  ray  of  light  which  impinges  obliquely  an  the  at- 
mosphere. Why  is  it  of  a  curvilinear  figure?  How  does  the  mind  judge 
of  the  position  of  an  object  ?  What  is,  therefore,  the  effect  of  astronomical 
refraction.'/  What  is  the  difference  in  this  respect  between  an  object  in 
the  horizon  and  one  in  the  zenith  ? 


ASTRONOMICAL  REFRACTION.          225 

increases,  and  ceasing  in  the  zenith.  An  object  seen  in 
the  zenith  is  therefore  in  its  true  position. 

On  these  principles,  the  figure  of  the  sun  and  moon, 
when  in  the  horizon,  changes  to  an  oval  shape ;  for  the 
lower  edge  being  more  acted  upon  than  the  upper,  is 
therefore  relatively  lifted  up,  and  those  objects  made  less 
in  their  vertical  dimensions  than  in  their  horizontal. 

Even  when  an  object  is  below  the  horizon  it  may  be 
so  much  elevated  as  to  be  brought  into  view;  for  just  in 
the  same  way  that  a  star,  R,  is  elevated  to  r,  so  may  one 
beneath  the  horizon  be  elevated  even  to  a  greater  extent, 
because  refraction  increases  as  we  descend  to  the  hori- 
zon. Stars,  therefore,  are  visible  before  they  have  ac- 
tually risen,  and  continue  in  sight  after  they  have  actually 
set.  They  are  thus  lifted  out  of  their  true  position  when 
in  the  horizon  about  thirty-three  minutes.  In  the  books  on 
astronomy  tables  are  given  which  represent  the  amount 
of  refraction  for  any  altitude. 

What  has  been  here  said  in  relation  to  a  star  holds  also 
for  the  sun  ;  which,  therefore,  is  made  apparently  to  rise 
sooner  and  set  later  than  what  is  the  case  in  reality. 
From  this  arises  the  important  result  that  the  day  is  pro- 
longed. In  temperate  climates,  this  lengthening  of  the 
day  extends  only  to  a  few  minutes,  in  the  polar  regions 
the  day  is  made  longer  by  a  month.  And  it  is  for  this 
cause,  too,  that  the  morning  does  not  suddenly  break  just 
at  the  moment  the  sun  appears  in  the  horizon,  and  the 
night  set  in  the  instant  he  sinks  ;  but  the  light  gradually 
fades  away,  as  a  twilight,  the  rays  being  bent  from  their 
path,  and  the  scattering  ones  which  fall  on  the  top  of  the 
atmosphere  brought  in  curved  directions  down  to  the 
lower  parts. 

The  phenomenon  of  twilight  is  not,  however,  wholly 
due  to  refraction.  The  reflecting  action  of  the  particles 
of  the  air  is  also  greatly  concerned  in  producing  it.  The 
manner  in  which  this  takes  place  is  shown  in  Fig.  252, 
where  A  B  C  D  represents  the  earth,  T  R  P  the  atmos- 
phere, and  S  O,  S'  N,  S"  A  rays  of  the  sun  passing  through 
it.  To  an  observer,  at  the  point  A,  the  sun,  at  S",  is  just 

Why  is  the  figure  of  the  sun  or  moon  oval  in  the  horizon  ?    What  is  to 
be  observed  as  respects  the  rising  and  setting  of  stars?    What  effect  has 
the  refraction  of  the  air  in  producing  twilight?    How  is  it  that  the  reflec- 
tive power  of  the  air  aids  in  this  effect  ? 
K* 


226  TWILIGHT. 


set,  but  the  whole  hemisphere  above  him,  P  R  T,  being 
his  sky,  reflects  the  rays  which  are  still  falling  upon  it, 
and  gives  him  twilight.  To  an  observer,  at  B,  the  sun 


Fig.  252. 
\0 
JM 


S" 

has  been  set  for  some  time,  and  he  is  in  the  earth's  shad- 
ow, but  that  part  of  his  sky  which  is  included  between  P 
Q,  R  x  is  still  receiving  sun-rays,  and  reflecting  them  to 
him.  To  an  observer  atC,  the  illuminated  portion  of  the 
sky  has  decreased  to  P  Q,  z.  His  twilight,  therefore, 
has  nearly  gone.  To  an  observer  at  D,  whose  horizon  is 
bounded  by  the  line  D  P,  the  sky  is  entirely  dark,  no 
rays  from  the  sun  falling  on  it.  It  is,  therefore,  night. 

The  action  of  the  atmosphere  sometimes  gives  rise  to 
curious  spectral  appearances — such  as  inverted  images, 
looming,  and  the  mirage.  The  latter,  which  often  occurs 
on  hot  sandy  plains,  was  frequently  seen  by  the  French 
during  their  expedition  to  Egypt,  giving  rise  to  a  decep- 
tive appearance  of  great  lakes  of  water  resting  on  the 
sands.  It  appears  to  be  due  to  the  partial  rarefaction  of 
the  lower  strata  of  air  through  the  heat  of  the  surface  on 
which  they  rest,  so  that  rays  of  light  are  made  to  pass  in 
a  curvilinear  path,  and  enter  the  eye.  In  the  same  way 
at  sea,  inverted  images  of  ships  floating  in  the  air  are 
often  discovered. 

Thus,  "On  the  1st  of  August,  1798,  Dr.  Vince  observ- 
ed at  Ramsgate  a  ship,  which  appeared,  as  at  A,  Fig.  253, 
the  topmast  being  the  only  part  of  it  seen  above  the  hori- 
zon. An  inverted  image  of  it  was  seen  at  B,  immediately 
above  the  real  ship,  at  A,  and  an  erect  image  at  C,  both 
of  them  being  complete  and  well  defined.  The  sea  was 

Describe  this  effect  in  the  four  positions,  A,  B,  C,  D  of  Fig.  252.  Men- 
tion some  remarkable  appearances  due  to  unusual  refraction  and  reflex- 
ion of  the  air. 


THE    MIRAGE. 


227 


Fig.  253. 


distinctly  seen  between  them,  as  at 
V  W.  As  the  ship  rose  to  the  ho- 
rizon, the  image,  C,  gradually  dis- 
appeared ;  and,  while  this  was  going 
on,  the  image  B,  descended,  but 
the  mainmast  of  B  did  not  meet  the 
mainmast  of  A.  The  two  images, 
B  C,  were  perfectly  visible  when 
the  whole  ship  was  actually  below 
the  horizon." 

These  singular  appearances,  which 
have  often  given  rise  to  superstitious 
legends,  may  be  imitated  artificially. 
Thus,  if  we  take  a  long  mass  of  hot 
iron,  and,  looking  along  the  upper 
surface  of  it  at  an  object  not  too 
distant,  we  shall  see  not  only  the 
object  itself,  but  also  an  inverted 
image  of  it  below,  the  second  im- 
age being  caused  by  the  refraction 
of  the  rays  of  .light  as  they  pass  through  the  stratum  of 
hot  air,  as  is  the  case  of  the  mirage. 

The  trembling  which  distant  objects  exhibit,  more  es- 
pecially when  they  are  seen  across  a  heated  surface,  is, 
in  like  manner,  due  to  unusual  aud  irregular  refraction 
taking  place  in  the  air. 


- 


LECTURE  XLVI. 


THE  ORGAN  OF  VISION. —  The  Three  Parts  of  the  Eye. — 
Description  of  the  Eye  of  Man. —  Uses  of  the  Accessory 
Apparatus. —  Optical  Action  of  the  Eye. —  Short  and 
Long-Sightedness. — Spectacles. — Erect  and  Double  Vis- 
ion.— Peculiarities  of  Vision. — Physiological  Colors. 

ALMOST  all  animals  possess  some  mechanism  by  which 
they  are  rendered  sensible  of  the  presence  of  light.  In 
some  of  the  lower  orders,  perhaps,  nothing  more  than  a 
diffused  sensibility  exists,  without  there  being  any  special 

How  may  the  mirage  be  imitated  ?  How  is  it  known  that  the  lowest  ani- 
mals are  sensible  to  light  ? 


22S 


THE    EYE. 


organ  adapted  for  the  purpose.  Thus,  many  animalcules 
are  seen  to  collect  on  that  side  of  the  liquid  in  which  they 
live  on  which  the  sun  is  shining,  and  others  avoid  the  light. 
But  in  all  the  higher  tribes  of  life  there  is  a  special  me- 
chanism, which  depends  for  its  action  on  optical  laws — it 
is  the  eye. 

This  organ  essentially  consists  of  three  different  parts — 
an  optical  portion,  which  is  the  eye,  strictly  speaking ;  a 
nervous  portion,  which  transmits  the  impressions  gather- 
ed by  the  former  to  the  brain  ;  and  an  accessory  portion, 
which  has  the  duty  of  keeping  the  eye  in  a  proper  work- 
ing state  and  defending  it  from  injury. 

In  man  the  eye-ball  is  nearly  of  a  spherical  figure,  be- 

jtlg  about  an  inch  in  di- 
ameter. As  seen  in  front, 
between  the  two  eyelids, 
d  c,  Fig.  254,  it  exhibits  a 
white  portion  of  a  porce- 
lain-like aspect,  a  a;  a  col- 
ored circular  part,  b  I, 
which  continually  changes 
in  width,  called  the  iris; 
and  a  central  black  por- 
d  tion,  which  is  tJie  pupil. 

When  it  is  removed  from  the  orbit  or  socket  in  which 
Fig.  255.  it  is  placed,  and  dissected,  the 

eye  is  found  to  consist  of  sever- 
al coats.  The  white  portion 
seen  anteriorly  at  a  a  extends 
all  round.  It  is  very  tough  and 
resisting,  and  by  its  mechanical 
qualities  serves  to  support  the 
more  delicate  parts  within,  and 
also  to  give  insertion  for  the  at- 
tachment of  certain  muscles 
which  roll  the  eye-ball,  and  direct  it  to  any  object. 
This  coat  passes  under  the  name  of  the  sclerotic.  It  is 
represented  in  Fig.  255,  at  a  a  a  a.  In  its  front  there 
is  a  circular  aperture,  into  which  a  transparent  portion, 
b  by  resembling  in  shape  a  watch-glass,  is  inserted.  This 

Of  how  many  parts  does  the  eye  consist  ?  What  are  the  offices  of 
these  parts  I  What  is  the  figure  and  size  of  the  eye  in  man  ?  What  is 
the  iris,  the  pupil,  and  the  sclerotic  coat  ? 


THE    EYE.  229 

This  is  called  the  cornea.  It  projects  somewhat  beyond 
the  general  curve  of  the  sclerotic,  as  seen  at  b  bt  in  the 
figure,  and  with  the  sclerotic  completes  the  outer  coat  of 
the  eye. 

The  interior  surface  of  the  sclerotic  is  lined  with  a  coat 
which' seems  to  be  almost  entirely  made  up  of  blood-ves- 
sels, little  arteries  and  veins,  which,  by  their  internetting, 
cross  one  another  in  evei'y  possible  direction.  It  is  called 
the  choroid  coat :  it  extends  like  the  sclerotic  as  far  as  the 
cornea.  Its  interior  surface  is  thickly  covered  with  a 
slimy  pigment  of  a  black  color,  hence  called  pigmentum 
nigrum.  Over  this  is  laid  a  very  delicate  serous  sheet, 
which  passes  under  the  name  of  Jacob's  membrane,  and 
the  optic  nerve,  O  O,  coming  from  the  brain  perforates  the 
sclerotic  and  choroid  coats,  and  spreads  itself  out  on  the 
interior  surface  as  the  retina,  rrrr.  The  optic  nerves  of 
the  opposite  eyes  decussate  one  another  on  their  passage 
to  the  brain. 

These,  therefore,  are  the  coats  of  which  the  eye  is  com- 
posed. Let  us  examine  now  its  internal  structure.  Be- 
hind the  cornea,  b  b,  there  is  suspended  a  circular  dia- 
phragm, ef,  black  behind  and  of  different  colors  in  differ- 
ent individuals  in  front.  This  is  the  iris.  Its  color  is,  in 
some  measure,  connected  with  the  color  of  the  hair.  The 
central  opening  in  it,  d,  is  the  pupil,  and  immediately  be- 
hind the  pupil,  suspended  by  the  ciliary  processes,  g  g,  is 
the  crystaline  lens,  c  c — a  double  convex  lens.  All  the 
space  between  the  anterior  of  the  lens  and  the  cornea  is 
filled  with  a  watery  fluid,  which  is  the  aqueous  humor ; 
that  portion  which  is  in  front  of  the  iris  is  called  the  an- 
terior chamber,  and  that  behind  it  the  posterior.  The  rest 
of  the  space  of  the  eye,  bounded  by  the  crystaline  lens 
in  front  and  the  retina  all  round,  is  filled  with  the  vitreous 
liumor,  V  V. 

With  respect  to  the  accessory  parts,  they  consist  chiefly 
of  the  eyelids,  which  serve  to  wipe  the  face  of  the  eye  and 
protect  it  from  accidents  and  dust;  the  lachrymal  appara- 
tus, which  serves  to  wash  it  with  tears,  so  as  to  keep  i» 

What  is  the  cornea 7  What  are  the  choroid  coat,  pigmentum  nigrum,  and 
Jacob's  membrane  ?  What  are  the  optic  nerve  and  retina  ?  What  is  the 
position  of  the  iris?  How  is  the  lens  supported  ?  Where  is  the  aqueous 
humor?  Where  the  vitreous  ?  What  are  the  two  chambers  of  the  eye  ? 
What  are  the  accessory  parts  and  their  uses  1 


230  SPECTACLES. 

continually  brilliant;  and  the  muscles  requisite  to  direct  it 
upon  any  point. 

Of  the  nervous  part  of  the  eye,  so  far  as  its  functions 
are  concerned,  but  little  is  known — the  retina  receives 
the  impressions  of  the  light,  and  they  are  conveyed  along 
the  optic  nerve  to  the  brain. 

Now  as  respects  the  optical  action  of  the  eye,  it  is  ob- 
viously nothing  more  than  that  of  a  convex  lens,  to  which, 
indeed,  its  structure  actually  corresponds :  and  as  in  ths 
focus  of  such  a  convex  lens  objects  form  images,  so  by  the 
conjoint  action  of  the  cornea  and  crystaline,  the  images  of 
the  things  to  which  the  eye  is  directed  form  at  the  proper 
focal  distance  behind — that  is,  upon  the  retina.  Distinct 
vision  only  takes  place  when  the  cornea  and  the  lens  have 
such  convexities  as  to  bring  the  images  exactly  upon  the 
retina. 

In  early  life  it  sometimes  happens  that  the  curvature 
of  these  bodies  is  too  great,  and  the  rays  converging  too 
rapidly,  form  their  images  before  they  have  reached  the 
posterior  part  of  the  eye,  giving  rise  to  the  defect  known 
as  short-sightedness — a  defect  which  may  be  remedied  by 
putting  in  front  of  the  cornea  a  concave  glass  lens  of  such 
concavity  as  just  to  compensate  for  the  excess  of  the  con- 
vexity of  the  eye. 

In  old  age,  on  the  contrary,  the  cornea  and  the  lens  be- 
come somewhat  flattened,  and  they  cannot  converge  the 
rays  soon  enough  to  form  images  at  the  proper  distance  be- 
hind. This  long-sightedness  may  be  remedied  by  putting 
in  front  of  the  cornea  a  convex  lens,  so  as  to  help  it  in  its 
action. 

Concave  or  convex  lenses  thus  used  in  front  of  the 
eyes  constitute  spectacles.  It  is  believed  that  this  appli- 
cation was  first  made  by  Roger  Bacon,  and  it  unquestion- 
ably constitutes  one  of  the  most  noble  contributions  which 
science  has  ever  made  to  man.  It  has  given  sight  to  mil- 
lions who  would  otherwise  have  been  blind. 

As  the  image  which  is  formed  by  a  convex  lens  is  in- 
verted as  respects  its  object,  so  must  the  images  which 
form  at  the  bottom  of  the  eye.  It  has,  therefore,  been  a 

What  is  the  duty  of  the  retina,  and  what  that  of  the  optic  nerve  ?  To 
what  optical  contrivance  is  the  eye  analogous  ?  When  does  distihct  vis- 
ion take  place?  What  is  the  cause  of  short-sightedness,  and  what  is  its 
cure  ?  What  is  the  cause  of  long-sightedness,  and  its  cure  ? 


PECULIARITIES    OF    VISION.  231 

question  among  optical  writers,  why  we  see  objects  in  their 
natural  position,  and  also  why  we  do  not  see  double,  inas- 
much as  we  have  two  eyes.  Various  explanations  of  these 
facts  have  been  offered,  chiefly  founded  upon  optical  prin- 
ciples. None,  however,  appear  to  have  given  general  sat- 
isfaction, and  in  reality  the  true  explanation,  I  believe, 
will  be  found  not  in  the  optical,  but  in  the  nervous  part 
of  the  visual  organ.  It  is  no  more  remarkable  that  we 
see  single,  having  two  eyes,  than  that  we  hear  single,  hav- 
ing two  ears.  It  is  the  simultaneous  arrival  in  the  brain, 
that  gives  rise  out  of  two  impressions  to  one  perception, 
and  accordingly,  when  we  disturb  the  action  of  one  of 
the  eyes  by  pressing  on  it,  we  at  once  see  double. 

Among  the  peculiarities  of  vision  it  maybe  mentioned, 
that  for  an  object  to  be  seen  it  must  be  of  certain  magni- 
tude, and  remain  on  the  retina  a  sufficient  length  of  time; 
arid,  for  distinct  vision,  must  not  be  nearer  than  a  certain 
distance,  as  eight  or  ten  inches.  This  distance  of  distinct 
vision  varies  somewhat  with  different  persons.  The  eye, 
too,  cannot  bear  too  brilliant  a  light,  nor  can  it  distinguish 
when  the  rays  are  too  feeble  ;  though  it  is  wonderful  to 
what  an  extent  in  this  respect  its  powers  range.  We  can 
read  a  book  by  the  light  of  the  sun  or  the  moon ;  yet  the 
one  is  a  quarter  of  a  million  times  more  brilliant  than  the 
other.  Luminous  impressions  made  on  the  retina  last  for 
a  certain  space  of  time,  varying  from  one  third  to  one 
sixth  of  a  second.  For  this  reason,  when  a  stick  with  a 
spark  of  fire  at  the  end  is  turned  rapidly  round,  it  gives 
rise  to  an  apparent  circle  of  light. 

By  accidental  or  physiological  colors  we  mean  such  as 
are  observed  for  a  short  time  depicted  on  surfaces,  and 
then  vanishing  away.  Thus,  if  a  person  looks  steadfastly 
at  a  sheet  of  paper  strongly  illuminated  by  the  sun,  and 
then  closes  his  eyes,  he  will  see  a  black  surface  corre- 
sponding to  the  paper.  So  if  a  red  wafer  be  put  on  a  sheet 
of  paper  in  the  sun.  and  the  eye  suddenly  turned  on  a 
white  wall,  a  green  image  of  the  wafer  will  be  seen. 
Spectral  illusions  in  the  same  way  often  arise — thus,  when 

Is  there  anything  remarkable  respecting  erect  and  double  vision? 
What  peculiarities  respecting  vision  may  be  remarked  ?  What  is  the 
distance  of  distinct  vision  ?  To  what  range  of  intensity  of  light  can  the 
eye  adapt  itself?  Why  does  a  lighted  stick  turned  round  rapidly  give  rise 
to  the  appearance  of  a  circle  of  fire  ?  What  is  meant  by  accidental  colors  ? 


232  OPTICAL  INSTRUMENTS. 

we  awake  in  the  morning,  if  our  eyes  are  turned  at  once 
to  a  window  brightly  illuminated,  on  shutting  them  again 
we  shall  see  a  visionary  picture  of  every  portion  of  the 
window,  which  after  a  time  fades  away. 


LECTURE  XL VII. 

OF  OPTICAL  INSTRUMENTS. —  The  Common  Camera  Ob- 
scura. —  The  Portable  Camera. —  The  Single  Microscope. 
—  The  Compound  Microscope. — Chromatic  and  Spheri- 
cal Aberration. —  The  Magic  Lantern, —  The  Solar  Mi- 
croscope.—  The  Oxyhydrogen  Microscope. 

IN  this  and  the  next  Lecture  I  shall  describe  the  more 
important  optical  instruments.  These,  in  their  external 
appearance,  and  also  iri  their  principles,  differ  very  much 
according  to  the  taste  or  ideas  of  the  artist.  The  descrip- 
tions here  given  will  be  limited  to  such  as  are  of  a  simple 
kind. 

THE  CAMERA  OBSCURA,  or  dark  chamber,  originally  con- 
sisted of  nothing  more  than  a  double  convex  lens,  of  a 
foot  or  two  in  focus,  fixed  in  the  shutter  of  a  dark  room. 
Opposite  the  lens  and  at  its  focal  distance,  a  white  sheet 
received  the  images.  These  represent  whatever  is  in  front 
©f  the  lens,  giving  a  beautiful  picture  of  the  stationary 
and  movable  objects  in  their  proper  relation  of  light  and 
shadow,  and  also  in  their  proper  colors. 

In  point  of  fact,  a  lens  is  not  required  :  for,  if  into  a 

Fig.  256. 


What  was  the  original  form  of  the  camera  obscura  ? 


CAMERA    OBSCURA.  233 

dark  chamber,  C  D,  Fig.  256,  rays  are  admitted  through 
a  small  aperture,  L,  an  inverted  image  will  be  formed  on 
a  white  screen  at  the  back  of  the  chamber,  of  whatever 
objects  are  in  front.  Thus  the  object,  A  B,  gives  the  in- 
verted image,  b  a.  These  images  are,  however,  dim,  ow- 
ing to  the  small  amount  of  light  which  can  be  admitted 
through  the  hole.  The  use  of  a  double  convex  lens  per- 
mits us  to  have  a  much  larger  aperture,  and  the  images  are 
correspondingly  brighter.  pig.  257. 

The   portable  , 

camera   obscura       n       c 

consists     of    an  a 

achromatic  dou-  d\ 
ble  convex  lens, 
a  a',  set  in  a  brass 
mounting  in  the 
front  of  a  box  consisting  of  two  parts,  of  which  c  c'  slides 
in  the  wider  one,  bb'.  The  total  length  of  the  box  is  ad- 
justed to  suit  the  focal  distance  of  the  lens.  In  the  back 
of  the  part,  c  c',  there  is  a  square  piece  of  ground  glass,  J, 
which  receives  the  images  of  the  objects  to  which  the 
lens  is  directed,  and  by  sliding  the  movable  part  in  or 
out  the  ground  glass  can  be  brought  to  the  precise  focus. 
The  interior  of  the  box  and  brass  piece,  a  a',  is  blackened 
all  over  to  extinguish  any  stray  light. 

The  images  of  the  camera  are,  of  course,  inverted,  but 
they  can  be  seen  in  their  proper  position  by  receiving 
them  on  a  looking-glass,  placed  so  as  to  reflect  them  up- 
ward to  the  eye.  Objects  that  are  near,  compared  with 
objects  that  are  distant,  require  the  back  of  the  box  to  be 
drawn  out,  because  the  foci  are  farther  off.  Moreover, 
those  that  are  near  the  edges  are  indistinct,  while  the  cen- 
tral ones  are  sharp  and  perfect.  This  arises  from  the  cir- 
cumstance that  the  edges  of  the  ground  glass  are  farther 
from  the  lens  than  the  central  portion,  and,  therefore,  out 
of  focus. 

OF    MICROSCOPES. 

The  single  microscope. — When  a  convex  lens  is  placed 

Is  it  necessary  to  have  a  lens  ?  What  advantage  arises  from  the  use  of 
one?  Describe  the  portable  camera  obscura.  Why  does  the  focal  dis- 
tance vary  for  different  objects?  Why  are  the  images  on  the  edges  indis- 
tinct while  the  central  ones  are  sharp  ? 


234 


THE    MICROSCOPE. 


Fig.  258. 


between  the  eye  and  an  object  situated  a  little  nearer  than 
its  focal  distance,  a  magnified  and  erect  image  will  be  seen. 

The  single  microscope  con- 
sists of  such  a  lens,  m,  Fig. 
258,  the  object,  b  c,  being  on 
one  side  and  the  eye,  «,  at 
the  other,  a  magnified  and 
erect  image,  B  C,  is   seen. 
The  linear  magnifying  pow- 
er of  such  a  lens  is  found  by 
dividing  the  distance  of  distinct  vision  by  its  focal  length. 
The  co?npound  microscope  commonly  consists  of  three 

lenses,  A  B,  E  F,  C  D, 

*'  Fig.  259;    A  B  being 

the  object-glass,  E  F  the 
field-glass,  and  C  D  the 
eye-glass.  Beyond  the 
object-glass  is  placed 
the  object,  at  a  dis- 

w  tance  somewhat  greater 

than  the  focal  length  ;  a  magnified  image  is,  therefore, 
produced,  and  this  being  viewed  by  the  eye-glass  is  still 
further  magnified,  and,  of  course,  seen  in  an  inverted  po- 
sition. The  use  of  the  field-glass  is  to  intercept  the  ex- 
treme pencils  of  light,  n  m,  coming  from  the  object-glass, 
which  would  otherwise  not  have  fallen  on  the  eye-lens. 
It  therefore^  increases  the  field  of  view,  and  hence  its 
name. 

In  this  instrument  the  object-glass  has  a  very  short  fo- 
cus, the  eye-glass  one  that  is  much  larger ;  and  the  field- 
glass  and  the  eye-glass  can  be  so  arranged  as  to  neutral- 
ize chromatic  aberration. 

To  determine  directly  the  magnifying  power  of  this  in- 
strument, an  object,  the  length  of  which  is  known,  is  placed 
before  it.  Then  one  eye  being  applied  to  the  instrument, 
with  the  other  we  look  at  a  pair  of  compasses,  the  points 
of  which  are  to  be  opened  until  they  subtend  a  space 
equal  to  that  under  which  the  object  appears.  This  space 
being  divided  by  the  known  length  of  the  object,  gives  the 
magnifying  power. 

Describe  the  single  microscope.  How  is  its  magnifying  power  found  ? 
Describe  the  compound  microscope.  What  is  the  use  of  the  field  lens  ? 
How  may  its  magnifying  power  be  found  ? 


COMPOUND    MICROSCOPE. 


235 


In  Fig.  260,  we  have  a  representation  of  the  compound 


Fig.  260. 


microscope,  as  commonly  made.  A 
B  is  a  sliding  brass  tube,  which  bears 
the  eye-glass  ;  m  n  is  the  object- 
glass  ;  I  K  the  field-glass  ;  S  T  a 
stage  for  carrying  the  objects.  It 
can  be  moved  to  the  proper  focal  dis- 
tance by  means  of  a  pinion.  At  V 
there  is  a  mirror  which  reflects  the 
light  of  a  lamp  or  the  sky  upward, 
to  illuminate  the  object.  The  body 
of  the  microscope  is  supported  on 
the  pillar  M,  and  it  can  be  turned 
into  the  horizontal  or  any  oblique  po- 
sition to  suit  the  observer,  by  a  joint, 
N.  To  the  better  kind  of  instru- 
ments micrometers  are  attached,  for 
the  purpose  of  determining  the  di- 


mensions of  objects.  These  are  some-  LI/ 


times  nothing  more  than  a  piece  of  glass,  on  which  fine 
lines  have  been  drawn  with  a  diamond,  forming  divisions 
the  value  of  which  is  known.  Such  a  plate  may  be  placed 
either  immediately  beneath  the  object  or  at  the  diaphragm, 
which  is  between  the  two  lenses. 

In  microscopes  the  defective  action  of  lenses,  known 
as  chromatic  aberration,  and  described  in  Lecture  XLL, 
interferes,  and,  by  imparting  prismatic  colors  to  the  edges 
of  objects,  tends  to  make  them  indistinct.  To  overcome 
this  difficulty,  achromatic  object-glasses  are  used  in  the 
finer  kinds  of  instruments. 

Besides  chromatic  aberration,  there  is  another  defect 
to  which  lenses  are  subject.  It  arises  from  their  spheri- 
cal figure,  and  hence  is  designated  spherical  aberration. 
Let  P  P,  Fig.  261,  be  a  convex  lens,  on  which  rays,  E  P, 
E  P,  E  M,  E  M,  E  A,  from  any  object,  E  e,  are  incident, 
it  is  obvious  that  the  principal  ray,  E  A,  will  pass  on, 
through  B,  to  F  without  undergoing  refraction.  Now, 
rays  which  are  near  to  this,  as  E  M,  E  M,  converge  by 
the  action  of  the  lens  to  a  focus  at  F  ;  but  those  which 
are  more  distant,  and  fall  near  the  edges  of  the  lens,  as 

Describe  the  parts  of  the  compound  microscope  represented  in  Fig.  260. 
What  kind  of  micrometers  may  be  used  ?  What  are  the  effects  of  chro- 
matic and  spherical  aberration  ? 


236 


MAGIC    LANTERN. 


E  N,  JS  N,  converge  more  rapidly,  and  come  to  a  focus 
at  G-.  Thus,  images,  F  ft  G  g,  are  formed  by  the  ex- 
treme rays,  and  an  intermediate  series  of  them  by  the 

Fig.  261. 


E 


intermediate  rays,  the  whole  arising  from  the  peculiarity 
of  figure  of  the  lens.  It  is,  indeed,  the  same  defect  as 
that  to  which  spherical  mirrors  are  liable,  as  explained 
in  Lecture  XXXVII ;  and  hence,  to  obtain  perfect  action 
with  a  spherical  lens,  as  with  a  spherical  mirror,  its  ap- 
erture must  be  limited. 

THE   MAGIC  LANTERN  consists  of  a  metallic  lantern, 

Fig.  262. 


A  A'  Fig.  262,  in  front  of  which  two  lenses  are  placed. 
One  of  these,  m,  is  the  illuminating  lens,  the  other,  n,  the 
magnifier.  A  powerful  Argand  lamp  is  placed  at  L,  and 
behind  it  a  concave  mirror,  p  q.  In  the  space  between 
the  two  lenses  the  tube  is  widened  c  d,  or  such  an  arrange- 
ment made  that  slips  of  glass,  on  which  various  figures 
are  painted,  can  be  introduced.  The  action  of  the  in- 
strument is  very  simple.  The  mirror  and  the  lens  m 

Describe  the  magic  lantern.     What  is  the  use  of  its  condensing  lens  and 
mirror  ? 


SOLAR    MICROSCOPE.  237 

illuminate  the  ^drawing  as  highly  as  possible ;  for  the 
lamp  being  placed  in  their  foci,  they  throw  a  brilliant 
light  upon  it,  and  the  magnifying  lens,  n,  which  can  slide 
in  its  tube  a  little  backward  and  forward,  is  placed  in 
such  a  position  as  to  throw  a  highly  magnified  image  of 
the  drawing  upon  a  screen,  several  feet  off,  the  precise 
focal  distance  being  adjusted  by  sliding  the  lens.  As  it 
is  an  inverted  image  which  forms,  it  is,  of  course,  neces- 
sary to  put  tke  drawing  in  the  slide,  c  d,  upside  down,  so 
as  to  have  their  images  in  the  natural  position.  Various 
amusing  slides  are  prepared  by  the  instrument-makers, 
some  representing  bodies  or  parts  in  motion.  The  fig- 
ures require  to  be  painted  in  colors  that  are  quite  trans- 
parent. 

THE  SOLAR  MICROSCOPE. — This  instrument,  like  the 


magic  lantern,  consists  of  two  parts — one  for  illuminating 
the  object  highly,  and  the  other  for  magnifying  it.  It 
consists  of  a  brass  plate,  which  can  be  fastened  to  an 
aperture  in  the  shutter  of  a  dark  room,  into  which  a  beam 
of  the  sun  may  be  directed  by  means  of  a  plane  mirror. 
In  Fig.  263,  M  is  the  mirror,  to  which  movement  in  any  di- 
rection may  be  given  by  the  two  buttons,  X  and  Y,  that  rays 
from  the  sun  may  be  reflected  horizontally  into  the  room. 
They  pass  through  a  large  convex  lens,  R,  and  are  con- 
converged  by  it ;  they  again  impinge  on  a  second  lens, 
U  S,  which  concentrates  them  to  a  focus,  the  precise 
point  of  which  may  be  adjusted  by  sliding  the  lens  to  the 
proper  position  by  the  button  B.  P  P'  is  in  apparatus, 
consisting  of  two  fixed  plates,  with  a  movable  one,  Q,  be- 
tween them,  Q,  being  pressed  against  P'  by  means  of 
spiral  springs.  This  apparatus  is  for  the  purpose  of  sup- 
porting the  various  objects  which  are  held  by  the  pressure 

Why  must  the  slider  be  put  in  upside  down  ?  What  are  the  two  parts 
of  the  solar  microscope?  Describe  the  instrument  as  represented  in 
Fig.  263. 


238  OXYIIYDROGEN    MICROSCOPE. 

of  Q,  against  P'.  Immediately  beyond  this,  at  L,  is  the 
magnifying  lens,  or  object-glass,  which  can  be  brought  to 
the  proper  position  from  the  highly  illuminated  object  by 
means  of  the  button  B',  and  the  magnified  image  result- 
ing is  then  thrown  on  a  screen  at  a  distance. 

The  solar  microscope  has  the  great  advantage  of  ex- 
hibiting objects  to  a  number  of  persons  at  the  same 
time. 

In  principle,  the  oxyhydrogen  microscope  is  the  same 
as  the  foregoing,  only,  instead  of  employing  the  light  of 
the  sun,  the  rays  of  a  fragment  of  lime  ignited  in  the 
flame  of  a  oxyhydrogen  blow-pipe  are  used.  These  rays 
are  converged  on  the  object,  and  serve  to  illuminate  it. 
The  advantage  the  instrument  has  over  the  solar  micro- 
scope is  that  it  can  be  used  at  night  and  on  cloudy  days. 


LECTURE  XLVIII. 

OF  TELESCOPES. — Refracting  and  Reflecting  Telescopes. 
— Galileo's  Telescope. —  The  Astronomical  Telescope. — 
The  Terrestrial. — Of  Reflecting  Telescopes. — Hersckel's 
Newton's,  Gregory's. — Determination  of  their  Magnify- 
ing Powers. —  The  Achromatic  Telescope. 

THE  telescope  is  an  instrument  which,  in  principle,  re- 
sembles the  microscope,  both  being  to  exhibit  objects  to 
us  under  a  larger  visual  angle.  The  microscope  does 
this  for  objects  near  at  hand,  the  telescope  for  those  that 
are  at  a  distance. 

Telescopes  are  of  two  kinds,  refracting  and  reflecting. 
Each  consists  essentially  of  two  parts,  the  object-glass  or 
objective,  and  the  eye-piece.  In  the  former,  the  objec- 
tive is  a  lens,  in  the  latter  it  is  a  concave  mirror. 

The  distinctness  of  objects  through  telescopes  is  neces- 
sarily connected  with  the  brilliancy  of  the  images  they 
give,  and  this,  among  other  things,  depends  on  the  size  of 
the  objective. 

What  advantage  has  the  solar  microscope  over  other  forms  of  instru. 
ment  ?  What  is  the  oxyhydrogen  microscope  ?  What  is  the  telescope  ? 
Of  how  many  kinds  are  telescopes  ?  What  are  their  essential  parts  ? 
What  is  the  objective  in  the  refracting  and  reflecting  telescope,  re- 
spectively  ?  On  what  does  the  brilliancy  depend  ? 


GALILEO  S    TELESCOPE. 


239 


There  are  three  kinds  of  refracting  telescopes  : — 1st, 
Galileo's ;  2d,  the  astronomical ;  3d,  the  terrestrial. 
GALILEO'S   TELESCOPE,  which  is  represented  in  Fig. 


264,  consists  of  a  convex  lens,  L  N,  which  is  the  objec- 
tive, and  a  concave  eye-glass,  E  E.  Let  O  B  be  a  dis- 
tant object,  the  rays  from  which  are  received  upon  L  N, 
and  by  it  would  be  brought  to  a  focus,  and  give  the  im- 
age, M  I ;  but,  before  they  reach  this  point,  they  are  in- 
tercepted by  the  concave  eye-glass,  E  E,  which  makes 
them  diverge,  as  represented  at  H  K,  and  give  an  erect 
image,  i  m. 

This  form  of  telescope  has  an  advantage  in  the  erect 
position  of  its  image,  which  is  usually  presented  with 
great  clearness.  Its  field  of  view,  by  reason  of  the  di- 
vergence of  the  rays  through  the  eye-glass,  is  limited. 
When  made  on  a  small  scale,  it  constitutes  the  common 
opera-glass. 

THE  ASTRONOMICAL  TELESCOPE  differs  from  the  former 


in  having  for  its  eye-piece  a  convex  lens  of  short  focus 
compared  with  that  of  the  object-lens.  In  this,  as  in  the 
former  instance,  the  office  of  the  objective  is  to  give  an 
image,  and  the  eye-piece  magnifies  it  precisely  on  the 
same  principle  that  it  would  magnify  any  object.  In  Fig. 
265,  L  N  is  the  objective,  and  E  E  the  eye-glass ;  the 
rays  from  a  distant  object,  O  B,  are  converged  so  as  to 
give  a  focal  image,  M  I.  This  being  viewed  through 
the  eye-lens,  E  E,  is  magnified,  and  is  also  inverted. 
The  magnifying  power  of  the  telescope  is  found  by  di- 

How  many  kinds  of  refracting  telescopes  are  there  ?  Describe  Galileo's 
telescope.  Why  has  it  so  small  a  field  of  view  ?  What  are  the  essential 
parts  of  the  astronomical  telescope  ?  Why  does  it  invert  ? 


240  TERRESTRIAL  TELESCOPE. 

viding  the  focal  length  of  the  objective  by  that  of  the  eye- 
lens. 

This  telescope,  of  course,  inverts,  and  therefore  is  not 
well  adapted  for  terrestrial  objects  ;  but  for  celestial  ones 
it  answers  very  well. 

THE  TERRESTRIAL  TELESCOPE  consists  of  an  object- 

Fig.  266. 

O 


lens,  like  the  foregoing,  but  in  its  eye-piece  are  three 
lenses  of  equal  focal  lengths.  The  combination  is  repre- 
sented in  Fig.  266,  in  which  L  N  is  the  object  lens,  and 
E  E,  F  F,  G  G  the  eye-lenses,  placed  at  distances  from 
each  other  equal  to  double  their  focal  length.  The  prog- 
ress of  the  rays  through  the  object-lens  and  the  first  eye- 
glass to  X  is  the  same  as  in  the  astronomical  telescope ; 
but,  after  crossing  at  X,  they  are  received  on  the  second 
eye-lens,  which  gives  an  erect  image  of  them,  at  i  m,  which 
is  viewed,  therefore,  in  the  erect  position  by  the  last  eye- 
lens,  G  G. 

As  the  distance  at  which  the  image  forms  from  the  ob- 
ject-lens is  dependent  on  the  actual  distance  of  the  object 
itself,  one  which  is  near  giving  its  image  farther  off  than 
one  which  is  distant,  it  is  necessary  to  have  the  means  of 
adjusting  the  eye-piece,  so  as  to  bring  it  to  the  proper  dis- 
tance from  the  image,  M  I.  The  object-lens  is  there- 
fore put  in  a  tube  longer  than  its  own  focus,  and  in  this 
a  smaller  tube,  bearing  the  three  eye-lenses,  immovably 
fixed,  slides  backward  and  forward  ;  this  tube  is  drawn  out 
until  distinct  vision  of  the  object  is  attained. 

REFLECTING  TELESCOPES  are  of  several  different  kinds. 
They  have  received  names  from  their  inventors. 

HERSCHEL'S  TELESCOPE  consists  of  a  metallic  concave 
mirror,  set  in  a  tube  in  a  position  inclined  to  the  axis.  It 
of  course  gives  an  inverted  image  of  the  object  at  its  fo- 
cus, and  the  inclination  is  so  managed  as  to  have  the  im- 
age form  at  the  side  of  the  tube.  There  it  is  viewed  by 

How  is  its  magnifying  power  found  ?  Describe  the  terrestrial  telescope. 
What  is  the  action  of  its  three  eye-lenses  ?  Why  must  there  be  means  of 
sliding  the  eye-piece  ?  How  are  reflecting  telescopes  designated  ?  De- 
scribe Herschel's  telescope. 


NEWTON'S  AND  GREGORY'S  TELESCOPES.        241 

an  eye-lens,  which  shows  it  magnified  and  inverted.  The 
back  of  the  observer  is  turned  to  the  object,  and  the  in- 
clmation  of  the  mirror  is  for  the  purpose  of  avoidino-  ob- 
struction of  the  light  by  the  head. 

NEWTON'S  TELESCOPE  consists  of  a  concave  mirror  A 
R,  Fig.  267,  with  its  axis  parallel  to  that  of  the  tube,  D  E 

Fig.  267 


F  G,  in  which  it  is  set.  The  rays  reflected  from  it  are 
intercepted  by  a  plane  mirror,  C  K,  placed  at  an  angle  of 
45°,  on  a  sliding  support,  m.  They  are,  therefore,  re- 
flected toward  the  side  of  the  tube,  the  image,  i  m,  form- 
ing at  I  M,  an  eye-glass  at  L  magnifies  it. 

THE  GREGORIAN  TELESCOPE  has  a  concave  mirror,  A  R, 
Fig.  268,  with  an  aperture,  L,  in  its  center.     The  rays 

Fif.268. 

A  o 


from  a  distant  object,  O  B,  give,  as  before,  an  inverted 
image,  M  I.  They  are  then  received  on  a  small  concave 
mirror,  K  C,  placed  fronting  the  great  one.  This  gives 
an  erect  image,  which  is  magnified  by  the  eye-lens,  P. 

The  magnifying  power  of  any  of  these  instruments  may 
be  roughly  estimated  by  looking  at  an  object  through  them 
with  one  eye,  and  directly  at  it  with  the  other,  and  com- 
paring the  relative  magnitude  of  the  two  images.  In  Her- 
schel's  telescope  the  back  of  the  observer  is  toward  the 
object,  in  Newton's  his  side,  but  in  Gregory's  he  looks  di- 
rectly at  it.  The  latter  is,  therefore,  by  far  the  most 
agreeable  instrument  to  use.  The  largest  telescopes  hith- 
erto constructed  are  upon  the  plan  of  Herschel  and 
Newton. 

When  Sir  Isaac  Newton  discovered  the  compound  na- 
ture of  light,  by  prismatic  analysis,  he  came  to  the  con- 
In  what  position  does  the  observer  stand  ?  Describe  Newton's  telescope 
Describe  the  Gregorian  telescope.    How  may  the  magnifying  power  of 
these  instruments  be  ascertained  ? 


242  THE    ACHROMATIC    TELESCOPE. 

elusion  that  the  refracting  telescope  could  never  be  a  per- 
fect instrument,  because  it  appeared  impossible  to  form 
an  image  by  a  convex  lens,  without  its  being  colored  on 
the  edges  by  the  dispersion  of  light.  He  therefore  turn- 
ed his  attention  to  the  reflecting  telescope,  and  invented 
the  one  which  bears  his  name.  He  even  manufactured 
one  with  his  own  hands.  It  is  still  preserved  in  the  cab- 
inet of  the  Royal  Society  of  London. 

But  after  it  was  discovered  that  refraction  without  dis- 
persion can  be  effected,  and  that  lenses  can  be  made  to 
form  colorless  images  in  their  foci,  the  principle  was  at 
once  applied  to  the  telescope ;  and.  hence  originated  that 
most  valuable  astronomical  instrument,  the  achromatic 
telescope. 

-  In  this  the  object-glass  is  of  course  compound,  consist- 
ing, as  represented  in  Fig.  269,  of  one  crown  and  one 

Fig.  269.  Fig.  270. 


flint-glass  lens,  or  as  represented  in  Fig.  270,  of  one  flint 
and  two  crown-glass  lenses.  The  principle  of  its  action  has 
been  described  in  Lecture  XLI.  The  great  expense  of 
these  instruments  arises  chiefly  from  the  costliness  of  the 
flint-glass,  for  it  has  hitherto  been  found  difficult  to  obtain 
it  in  masses  of  large  size,  perfectly  free  from  veins  or 
other  imperfections.  Nevertheless,  there  are  instruments 
which  have  been  constructed  in  Germany,  with  an  aper- 
ture of  thirteen  inches.  Some  of  these  are  mounted  on 


.Tiiat  wao  it  van  IKU  LU  me  adoption  oi  tne  renecting  telescope  i  un 
what  does  the  achromatic  telescope  depend  ?  Of  what  parts  are  the  dou- 
ble and  triple  object-glasses  composed  ?  What  is  the  cause  of  the  costli- 


ness of  these  instruments  ? 


ACHROMATIC  TELESCOPES.  243 

a  frame,  connected  with  a  clock  movement,  so  that  when 
the  telescope  js  turned  to  a  star  it  is  steadily  kept  in  the 
center  of  the  field  of  view,  notwithstanding  the  motion  of 
the  earth  on  her  axis.  Several  large  instruments  of  this 
description  are  now  in  the  different  observatories  of  the 
United  States. 


244  HEAT    OR    CALORIC. 


THE  PROPERTIES  OF  HEAT. 

THERMOTICS. 


LECTURE  XLDL 

THE  PROPERTIES  OF  HEAT. — Relations  of  Light  and  Heat. 
— Mode  of  Determining  the  Amount  of  Heat.— The 
Mercurial  Thermometer. — Its  Fixed  Points. — Fahren- 
keit's,  Centigrade,  Reaumur's  Thermometers. —  The  Gas 
Thermometer. — Differential  Thermometer. — Solid  Ther- 
mometers.— Comparative  Expansion  of  Gases,  Liquids, 
and  Solids. 

WHATEVER  may  be  the  true  cause  of  light,  whether  it 
be  undulations  in  an  ethereal  medium,  or  particles  emit- 
ted with  great  velocity  by  shining  bodies,  observation  has 
clearly  proved  that  heat  is  closely  allied  to  it. 

When  a  body  is  brought  to  a  very  high  temperature, 
and  then  allowed  to  cool  in  a  dark  place,  though  it  might 
be  white-hot  at  first  it  very  soon  becomes  invisible,  losing 
its  light  apparently  in  the  same  way  that  its  loses  its  heat. 
And  we  shall  hereafter  find  the  rays  of  heat  which  thus 
escape  from  it  may  be  reflected,  refracted,  inflected,  and 
polarized,  just  as  though  they  were  rays  of  light. 

In  its  general  relations  heat  is  of  the  utmost  importance 
in  the  system  of  nature.  The  existence  of  life,  both  vege- 
table and  animal,  is  dependent  on  it;  it  determines  the 
dimensions  of  all  objects,  regulates  the  form  they  assume, 
and  is  more  or  less  concerned  in  every  chemical  change 
that  takes  place. 

Every  object  to  which  we  have  access  possesses  a  cer- 
tain amount  of  heat,  and  so  long  as  it  remains  at  common 

What  is  observed  during  the  cooling  of  bodies  ?  Why  are  the  relations 
of  heat  of  such^philosophical  importance  ? 


THE    THERMOMETER. 


245 


temperatures,  may  be  touched  without  pain  ;  but  if  a  larg- 
er quantity  of  heat  is  given  to  it,  it  assumes  qualities  that 
are  wholly  new,  and  if  touched  it  burns. 

To  determine,  therefore,  with  precision  the  quantity  of 
heat  which  is  present  in  a  body  when  it  exhibits  any 
particular  phenomenon,  it  is  necessary  that  we  should  be 
furnished  with  some  means  of  effecting  its  measurement. 
Instruments  intended  for  this  purpose  are  called  ther- 
mometers. 

Of  thermometers  we  have  several  different  kinds.  Some 
are  made  of  solid  substances,  others  of  liquids,  and  others 
of  gases.  With  a  few  exceptions,  they  all  depend  on  the 
same  principle — the  expansion  which  ensues  in  all  bodies 
as  their  temperature  rises. 

Of  these  the  mercurial  thermometer  is  the  most  F*g-  271 
common,  and  for  the  purpose  of  science  the  most' 
generally  available.  It  consists  of  a  glass  tube, 
Fig,  271,  with  a  bulb  on  its  lower  extremity. 
The  entire  bulb  and  part  of  the  tube  are  filled 
with  quicksilver,  and  the  rest  of  the  tube,  the  ex- 
tremity of  which  is  closed,  contains  a  vacuum. 
This  glass  portion  is  fastened  in  an  appropriate 
manner,  upon  a  scale  of  ivory  or  metal,  which 
bears  divisions,  and  the  thermometer  is  said  to  be 
at  that  particular  degree  against  which  its  quick- 
silver stands  on  the  scale. 

If  we  take  the  bulb  of  such  an  instrument  in 
the  hand,  the  quicksilver  immediately  begins  to 
rise  in  the  tube,  and  finally  is  stationary  at  some 
particular  degree,  generally  the  98th  in  our  ther- 
mometers. We  therefore  say  the  temperature  of 
the  hand  is  98  degrees. 

In  effecting  a  measure  of  any  kind,  it  is  neces- 
sary to  have  a  point  from  which  to  stait  and  a 
point  to  which  to  go.  The  same  is  also  necessa- 
ry in  making  a  scale.  One  of  the  essential  qual- 


ities of  a  thermometer  is  to  enable  observers  in  all  parts 
of  the  world  to  indicate  the  same  temperature  by  the  same 


What  is  the  use  of  the  thermometer?  What  different  kinds  of  ther- 
mometers have  we  ?  On  what  general  principle  do  they  all  depend  ?  What 
form  of  thermometer  is  the  most  common  ?  What  are  the  degrees  ?  What 
temperature  does  it  indicate  if  held  in  the  hand?  Why  are  fixed  points 
necessary  in  forming  the  scale  ? 


246  THERMOMETRIC    SCALES. 

degree.  A  common  system  of  dividing  the  scale  must, 
therefore,  be  agreed  upon,  that  all  thermometers  may  cor- 
respond. 

If  we  dip  a  thermometer  in  melting  ice  or  snow,  the 
quicksilver  sinks  to  a  certain  point,  and  to  this  point  it 
will  always  come,  no  matter  when  or  where  the  experi- 
ment is  made.  If  we  dip  it  in  boiling  water,  it  at  once 
rises  to  another  point.  Philosophers  in  all  countries  have 
agreed  that  these  are  the  best  fixed  points  to  regulate  the 
scale  by,  and  accordingly  they  are  now  used  in  all  ther- 
mometers. In  the  Fahrenheit  thermometer,  which  is  com- 
monly employed  in  the  United  States,  we  mark  the  point 
at  which  the  instrument  stands,  when  dipped  in  melting 
snow,  32°,  and  that  for  boiling  water,  212°,  and  divide  the 
intervening  space  into  180  parts,  each  of  which  is  a  de- 
gree ;  and  these  degrees  are  carried  up  to  the  top  and 
down  to  the  bottom  of  the  scale. 

In  other  countries  other  divisions  are  used,  adjusted, 
however,  by  the  same  fixed  points.  The  Centigrade 
thermometer  has,  for  the  melting  of  ice,  0,  and  for  the 
boiling  of  water,  100°,  with  the  intervening  space  divid- 
ed in  100  equal  degrees.  In  Reaumur's  thermometer, 
the  lower  point  is  marked  0,  and  the  upper  80°. 

The  philosophical  fact  upon  which  the  construction  of 
the  thermometer  reposes,  is  that  quicksilver  expands  by 
an  increase  of  heat,  and  is  contracted  by  a  diminution  of 
it;  and  further,  that  these  expansions  and  contractions  are 
in  proportion  to  the  changes  of  temperature. 

3ut  for  particular  purposes,  thermometers  have 
been  made  of  oil,  of  alcohol,  and  of  a  great  many 
other  liquid  bodies,  and  give  rise  to  the  same  gen- 
eral results.  As  an  uniform  law  it  may,  therefore, 
be  asserted  that  all  liquids  dilate  as  their  temper- 
ature rises,  and  contract  as  it  descends. 

But  heat  determines  the  volume  of  gases  as  well 
as  of  liquids.  If  we  take  a  tube,  a,  Fig.  272,  with 
a  bulb  at  its  upper  extremity,  &,  and  having  partly 
filled  the  tube  with  a  column  of  water,  colored,  to 
make  its  movements  visible,  the  lower  end  dipping 

What  two  fixed  points  have  been  selected  ?  What  is  the  Centigrade 
scale  ?  What  is  Reaumur's  scale  ?  What  is  the  fact  on  which  the  con- 
struction of  the  thermometer  depends  ?  How  may  this  be  extended  to 
other  liquids  ? 


AIR    THERMOMETER.  '  .        247 

loosely  into  some  of  the  same  colored  water,  contained  in 
a  bottle,  c;  on  touching  the  bulb,  b,  the  colored  liquid  in 
the  tube  is  pressed  down  by  the  dilatation  of  the  air,  and 
on  cooling  the  bulb  the  liquid  rises,  because  the  air  con- 
tracts. And  were  the  bulb  filled  with  any  other  gaseous 
substance,  such  as  oxygen,  hydrogen,  &c.,  still  the  same 
thing  would  take  place.  So  gases,  like  liquids,  expand 
as  their  temperature  rises,  and  contract  as  it  descends. 

Such  an  instrument  as  Fig.  272,  passes  under  the  name 
of  an  air  thermometer.  Its  indications  are  not  altogether 
reliable,  as  may  be  proved  by  putting  it  under  an  air-pump 
receiver,  when  its  column  of  liquid  will  instantly  move  as 
soon  as  the  least  change  is  made  in  the  pressure  of  the  air. 
It  is  affected,  therefore,  by  changes  of  pressure  as  well  as 
changes  of  temperature. 

There  is,  however,  a  form  of 
air  thermometer  which  is  free 
from  this  difficulty.  It  is  the  dif- 
ferential thermometer.  This  in- 
strument consists  of  a  tube,  a 
Fig.  273,  bent  at  right  angles  to- 
ward its  ends,  which  terminate 
in  two  bulbs,  c  d.  In  the  hori- 
zontal part  of  the  tube  is  a  little  column  of  liquid  marked 
by  the  black  line,  which  serves  as  an  index.  If  the  bulb 
c,  is  touched  by  the  hand,  its  air  dilates  and  presses  the 
index  column  over  the  scale ;  if  d  is  touched  the  same 
thing  takes  place,  but  the  column  moves  the  opposite 
way ;'  if  both  bulbs  are  touched  at  once,  then  the  column, 
pressed  equally  in  opposite  directions,  does  not  move  at 
all.  Of  course,  a  similar  reasoning  applies  to  the  cooling 
of  the  bulbs.  The  instrument  is,  therefore,  called  a  di£ 
ferential  thermometer,  because  it  indicates  the  difference 
of  temperature  between  its  bulbs,  but  not  absolute  tem- 
peratures to  which  it  is  exposed. 

In  the  same  manner  that  we  have  thermometers,  in 
which  the  changes  of  volume  of  liquids  and  gases  are 
employed,  to  indicate  changes  of  temperature,  so,  too,  we 
have  others  in  which  solids  are  used.  These  generally 
consist  of  a  strip  of  metal  which  is  connected  with  an  ar- 

How  may  it  be  extended  to  all  the  gases  ?  Describe  the  air  thermome- 
ter. Describe  the  differential  thermometer.  What  does  this  instrument 
indicate '? 


248 


EXPANSION    OF    LIQUIDS. 


Fig.  274. 


rangement  of  levers  or  wheels,  by  which  any  variations 
in  its  length  may  be  multiplied.  The  disturbing  agencies, 
thus  introduced  by  this  necessary  mechanism,  interfere 
very  much  with  the  exactness  of  these  instruments.  And 
hitherto  they  have  not  been  employed,  except  for  special 
purposes,  and  can  never  supplant  the  mercurial  thermom- 
eter. 

It  being  thus  established  that  all  substances,  gases, 
liquids,  and  solids  expand  as  their  temperature  rises,  and 
contract  as  it  falls,  it  may  next  be  remarked  that  great 
differences  are  detected  when  different  bodies  of  the  same 
form  are  compared.  There  are  scarcely  two  solid  sub- 
stances which,  for  the  same  elevation  of  temperature,  ex- 
pand alike.  All  do  expand  ;  but  some  more  and  some 
less.  In  the  case  of  crystalline  bodies,  even  the  same 
substance  expands  differently  in  different  directions. 
Thus,  a  crystal  of  Iceland  spar  dilates  less  in  the  direc- 
tion of  its  longer  than  it  does  in  the  direction  of  its  short- 
er axis.  The  same  holds  good  for  liquids.  If  a  number  of 
thermometers,  a  b  c,  Fig.  274,  of  the 
same  size  be  filled  with  different 
liquids,  and  all  plunged  in  the  same 
vessel  of  hot  water,  f,  so  as  to  be 
warmed  alike,  the  expansion  they 
exhibit  will  be  very  different.  Until 
recently,  it  was  believed  that  .all 
|  _V-  V^jl  oases  expand  alike  for  the  same 

^  changes  of  temperature,  but  it  is  now 
known  that  minute  differences  exist  among  them  in* this 
respect.  For  every  degree  of  Fahrenheit's  thermometer 
atmospheric  air  expands  Ti^-  of  its  volume  at  32°. 

Gases,  liquids,  and  solids  compared  together,  for  the 
same  change  of  temperature,  exhibit  very  different  changes 
of  volume ;  gases  being  the  most  dilatable,  liquids  next, 
and  solids  least  of  all.  This,  probably,  arises  from  the 
fact  that  the  cohesive  force,  which  is  the  antagonist  of 
heat,  is  most  efficient  in  solids,  less  so  in  liquids,  and  still 
less  in  gases. 

Are  thermometers  ever  made  of  solid  bodies  ?  What  difficulties  are  in 
the  way  of  their  use  ?  Do  bodies  of  the  same  form  expand  alike  ?  What 
remarks  may  be  made  respecting  Iceland  spar?  How  may  it  be  proved 
that  different  liquids  expand  differently  ?  What  is  the  expansion  of  air 
for  each. degree?  Do  other  gases  expand  exactly  like  air?  Of  gases, 
liquids,  and  solids,  which  expands  most  ? 


a 

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-f 

.      j 

RADIANT    HEAT.  249 


LECTURE  L. 

OP  RADIANT  HEAT.— Path  of  Radiant  Heat. —  Velocity 
of  Radiant  Heat. — Effects  of  Surface. — Law  of  Reflex- 
ion.— Reflexion  by  Spherical  Mirrors. —  Theory  of  Ex- 
changes of  Heat. —  Diathermanou$  and  Athermanous 
Bodies. — Properties  of  Rock  Salt. — Imaginary  Colora- 
tion. 

EXPERIENCE  shows  that  whenever  a  hot  body  is  freely 
exposed  its  temperature  descends,  until  eventually  it 
comes  down  to  that  of  the  surrounding  bodies.  There 
are  two  causes  which  tend  to  produce  this  result.  They 
are  radiation  and  conduction. 

All  bodies,  whatever  their  temperature  may  be,  radiate 
heat  from  their  surfaces.  It  passes  forth  in  straight  lines, 
and  may  be  reflected,  refracted,  and  polarized  like  light. 

The  rate  at  which  radiant  heat  moves  is,  in  all  proba- 
bility, the  same  as  the  rate  for  light.  It  has  been  asserted 
that  its  velocity  is  only  four  fifths  that  of  light,  but  this 
seems  not  to  rest  upon  any  certain  foundation. 

As  respects  the  rapidity  or  facility  with  which  radi- 
ation takes  place,  much  depends  on  the  nature  of  the  sur- 
face. The  experiments  of  Leslie  show  that,  at  equal 
temperatures,  such  as  are  smooth  are  far  less  effective 
than  such  as  are  rough. 
This  result  he  established 
by  taking  a  cubical  metal- 
lic vessel,  a,  filled  with 
hot  water,  the  four  verti- 
cal sides  being  in  differ- 
ent physical  conditions — 
one  being  polished,  a  sec- 
ond slightly  roughened,  a 
third  still  more  so,  and  the  fourth  roughened  and  black- 
ened. Under  these  circumstances,  the  rays  of  heat  es- 

What  causes  tend  to  produce  the  cooling  of  bodies  ?  In  what  direction 
does  radiant  heat  pass  ?  What  is  the  velocity  of  its  movement  ?  How  is 
the  rapidity  of  radiation  controlled  by  surface?  Of  smooth  and  rough 
bodies  which  are  the  best  radiators  ? 


250 


REFLEXION    OF    HEAT. 


caping  from  each  surface  as  it  was  turned  in  succession 
toward  a  metallic  reflector,  M,  raised  a  thermometer,  d, 
placed  in  the  focus,  to  very  different  degrees,  the  polished 
one  producing  the  least  effect. 

Just  as  light  is  reflected,  so,  too,  is  heat.  If  we  take  a 
plate  of  bright  tin  and  hold  it  in  such  a  position  as  to  re- 
flect the  light  of  a  clear  fire  into  the  face,  as  soon  as  we  see 
the  light  we  also  feel  the  impression  of  the  heat.  The 
law  for  the  one  is  also  the  law  for  the  other,  "  the  angle 
of  reflexion  is  equal  to  the  angle  of  incidence,"  and  con- 
sequently mirrors  with  curved  surfaces  act  precisely  in 
one  case  as  they  do  in  the  other.  We  have  already 
shown,  Lecture  XXXVII,  how  rays  diverging  from  tine 
focus  of  a  mirror  are  reflected  parallel,  and  how  parallel 
rays  falling  on  a  mirror  are  converged.  And  it  is  upon 
that  principle  that  we  account  for  the  following  striking 
experiment.  In  the  focus  of  a  concave  metallic  mirror 

Fig.  276. 


let  there  be  placed  a  red  hot  ball,  <z,  Fig.  276,  the  rays 
of  heat  diverging  from  it  in  right  lines,  a  c,  a  d,  a  e,  af 
will  be  reflected  parallel  in  the  lines  c  g,  d  h,  e  i,fk,  and, 
striking  upon  the  opposite  mirror,  will  all  converge  to  b, 
in  its  focus.  If,  therefore,  at  this  point  any  small  com- 
bustible body,  as  a  piece  of  phosphorus,  be  placed,  it 
will  instantly  take  fire,  though  a  distance  of  twenty  or  fifty 
feet  may  intervene  between  the  mirrors.  Or,  if  the  bulb 
of  an  air  thermometer  be  used  instead  of  the  phosphorus, 

What  is  the  law  for  the  reflexion  of  heat  ?     How  do  curved  mirrors 
act  on  radiant  heat  ?    Describe  the  experiment  represented  by  Fig.  276. 


THEORY  OF  THE  EXCHANGES  OP  HEAT.     251 

it  will  give  at  once  the  indication  of  a  rapid  elevation  of 
temperature. 

But  this  is  not  all;  for,  if  still  retaining  the  thermome- 
ter in  its  place,  we  remove  away  the  red  hot  ball  and  re- 
place it  by  a  mass  of  ice,  the  thermometer  instantly  indi- 
cates a  descent  of  temperature,  the^production  of  cold. 
At  one  time  it  was  supposed  that  this  was  due  to  cold 
rays  which  escaped  from  the  ice,  after  the  same  manner 
as  rays  of  heat,  but  it  is  now  admitted  that  the  effect 
arises  from  the  circumstance  that  the  thermometer  bulb, 
being  warmer  than  the  ice,  radiates  its  heat  to  the  ice, 
the  temperature  of  which  ascends  precisely  in  the  same 
manner  as  that  in  the  former  experiment,  the  red  hot 
ball  being  the  warmer  body,  radiated  its  heat  to  the  ther- 
mometer. 

In  fact,  these  experiments  are  nothing  more  than  illus- 
trations of  a  theory  which  passes  under  the  name  of"  the 
Theory  of  the  Exchanges  of  Heat."  This  assumes  that 
all  bodies  are  at  all  times  radiating  heat  to  one  another ; 
but  the  speed  with  which  they  do  this  depends  upon  their 
temperature,  a  hot  body  giving  out  heat  much  faster  than 
one  the  temperature  of  which  is  lower.  If  thus,  we  have 
a  red  hot  ball  and  a  thermometer  bulb  in  presence  of  one 
another,  the  ball,  by  reason  of  its  high  temperature,  will 
give  more  heat  to  the  bulb  than  it  receives  in  return  ;  its 
temperature  will,  therefore,  descend,  while  that  of  the 
bulb  rises.  But  if  the  same  bulb  be  placed  in  presence 
of  a  mass  of  ice,  the  ice  will  receive  more  heat  than  it 
gives,  because  it  is  the  colder  body  of  the  two,  and  the 
temperature  of  the  thermometer  therefore  declines. 

All  bodies  are  at  all  times  radiating  heat,  their  power  of 
radiation  depending  on  their  temperature,  increasing  as 
it  increases,  and  diminishing  as  it  diminishes. 

As  is  the  case  with  light,  so,  too,  with  heat :  there  are 
substances  which  transmit  its  rays  with  readiness,  and 
others  which  are  opaque.  "We  therefore  speak  of  dia- 
thermanous  bodies  which  are  analogous  to  the  trans- 
parent, and  athermanous  which  are  like  the  opaque. 

What  ensues  if  a  piece  of  ice  is  used  instead  of  a  hot  ball  ?  How  was  this 
formerly  explained  ?  What  is  the  true  explanation  of  it  ?  What  is  meant 
by  the  Theory  of  the  Exchanges  of  Heat  ?  On  what  does  the  rate  of  ra- 
diation depend?  What  are  dlathermaiious  bodies ?  What  axe  atherma- 
nous ones? 


252  REFRACTION    OF    HEAT. 

Among  the  former  a  vacuum  and  most  gaseous  bodies 
may  be  numbered ;  but  it  is  remarkable  that  substances 
which  are  perfectly  transparent  to  light  are  not  necessa- 
rily so  to  heat.  Glass,  which  transmits  with  but  little 
loss  much  of  the  light  which  falls  on  it,  obstructs  much  of 
the  heat ;  and,  conversely,  smoky  quartz  and  brown  mica 
which  are  almost  opaque  to  light  transmit  heat  readily. 
But  of  all  solid  substances,  that  which  is  most  transparent 
to  heat,  or  most  diathermanous,  is  rock-salt ;  it  has  there- 
fore been  designated  as  the  glass  of  radiant  heat.  If  a 
prism  be  cut  from  this  substance,  and  a  beam  of  radiant 
heat  allowed  to  fall  upon  it,  it  undergoes  refraction  arid 
dispersion  precisely  as  we  have  already  described  as 
occurring  under  similar  circumstances  with  a  glass  prism 
for  light  in  Lecture  XL.  And  if  convex  lenses  be 
made  of  rock-salt  they  converge  the  rays  of  heat  to  foci, 
at  which  the  elevation  of  temperature  may  be  detected 
by  the  thermometer.  Heat,  therefore,  can  be  refracted 
arid  dispersed  as  easily  as  it  can  be  reflected. 

If  we  take  a  convex  lens  of  glass  and  one  of  rock-salt, 
and  cause  them  to  form  the  image  of  a  burning  candle  in 
their  foci,  it  will  be  found  on  examination  that  the  image 
through  the  rock-salt  is  hot,  but  that  through  the  glass 
can  scarcely  affect  a  delicate  thermometer.  This  experi- 
ment sets  in  a  clear  light  the  difference  in  the  relations 
between  glass  and  salt,  the  former  permitting  the  light 
to  pass  but  not  the  heat,  the  latter  transmitting  both 
together. 

When  light  is  dispersed  by  a  prism  the  splendid  phe- 
nomenon of  the  spectrum  is  seen.  But  in  the  case  of 
heat  our  organs  of  sight  are  constituted  so  that  we  cannot 
discover  its  presence,  and  therefore  fail  to  see  the  cor- 
responding result.  But  it  is  now  established  beyond  all 
doubt,  that  in  the  same  manner  that  there  are  modifica- 
tions of  light  giving  rise  to  the  various  colored  rays,  so, 
too,  there  are  corresponding  qualities  of  radiant  heat. 
Moreover,  it  has  been  fully  proved  that,  as  stained  glass 
and  colored  solutions  exert  an  effect  on  white  Iight7  ab- 
sorbing some  rays  and  letting  others  pass,  the  same  takes 
place  also  for  heat.  In  the  case  we  have  already  con- 
Mention  some  of  the  former.  Of  all  solid  bodies  which  is  the  most 
diathermanous  ?  What  is  to  be  observed  when  rock-salt  and  glass  are 
compared? 


IMAGINARY    COLORATION.  253 

sidered  of  the  imperfect  diathermancy  of  glass — the  true 
cause  of  the  phenomenon  is  the  coloration  which  the 
glass  possesses  as  respects  the  rays  of  heat,  and  inasmuch 
as  a  substance  may  be  perfectly  transparent  to  one  of 
these  agents  and  not  so  to  the  other,  so,  also,  a  body  may 
stop  or  absorb  a  given  ray  for  the  one  and  a  totally  dif- 
ferent one  for  the  other.  Glass  allows  all  the  rays  of 
light  to  pass  almost  equally  well,  but  it  obstructs  almost 
completely  the  blue  rays  of  heat.  The  coloration  of 
bodies,  which  has  already  been  described  as  arising  from 
absorption,  may,  therefore,  be  wholly  different  in  the  two 
cases ;  and  as  our  organs  do  not  permit  us  to  see  what  it 
is  in  the  case  of  heat,  and  we  have  to  rely  on  indirect 
evidence,  we  speak  of  the  imaginary  or  ideal  coloration 
of  bodies. 

If  heat  like  light,  as  there  are  reasons  for  believing, 
arises  in  vibratory  movements  which  are  propagated 
through  the  ether,  all  the  various  phenomena  here  de- 
scribed can  be  readily  accounted  for.  The  undulations 
of  heat  must  be  reflected,  refracted,  inflected,  undergo 
interference,  polarization,  &c.,  .as  do  the  undulations  of 
light,  the  mechanism  being  the  same  in  both  cases. 


LECTURE  LI. 

CONDUCTION  AND  EXPANSION. — Good  and  Bad  Conductors 
of  Heat. — Differences  among  the  Metals. — Conduction 
and  Circulation  in  Liquids.— Point  of  Application  of 
Heat. —  Case  of  Gases. — Expansion  of  Gases,  Liquids, 
and  Solids. — Irregularity  of  Expansion  in  Liquids  and 
Solids. —  Regularity  of  Gases.  — r-  Point  of  Maximum 
Density  of  Water. 

WHEN  one  end  of  a  metallic  bar  is  placed  in  the  fire, 
after  a  certain  time  the  other  has  its  temperature  ele- 
vated, and  the  heat  is  said  to  be  conducted.  It  finds  its 


What  reasons  are  there  for  supposing  that  radiant  heat  is  colored  ?  Do 
natural  bodies  possess  a  peculiar  coloration  for  heat  ?  What  is  meant  by 
ideal  or  imaginary  coloration  ?  If  heat  consists  of  ethereal  undulations  to 
what  effects  must  it  be  liable  ?  What  is  meant  by  the  conduction  of 
heat? 


254  CONDUCTION    OF    HEAT. 

way  from  particle  to  particle,  from  those  that  are  hot  to 
those  that  are  cold. 

But  if  a  piece  of  wood  or  of  earthenware  be  submitted 
to  the  same  trial  a  very  different  result  is  obtained.  The 
farther  end  never  becomes  hot,  proving,  therefore,  that 
some  bodies  are  good  and  others  bad  conductors  of 
heat. 

The  rapidity  with  which  this  conduction  from  particle 
to  particle  takes  place,  depends,  among  other  things,  upon 
their  difference  of  temperature.  Thus,  when  the  bulb  of 
a  thermometer  is  plunged  in  a  cup  of  hot  water,  for  the 
first  few  moments  its  column  runs  up  with  rapidity,  but 
as  the  thermometer  comes  nearer  to  the  temperature  of 
the  water,  the  heat  is  transmitted  to  it  more  slowly. 

Of  the  three  classes  of  bodies  solids  are  the  best  con- 
ductors, liquids  next,  and  gases  worst  of  all.  Of  solids 
the  metals  are  the  best,  and  among  the  metals  may  be 
mentioned  gold,  silver,  copper.  Among  bad  solid  con- 
ductors we  have  charcoal,  ashes,  fibrous  bodies,  as  cotton, 
silk,  wool,  &c. 

That  the  metals  differ  very  much  in  this  respect  from 
one  another  may  be  satisfactorily  proved  by  taking  a  rod 
of  copper,  one  of  brass,  and  one  of  iron,  b  c  d.  Fig.  277, 
Fiff.277.  of  equal  length  and  diameter,  and  screw- 
ing them  into  a  solid  metallic  ball,  «,  hav- 
ing  placed  on  their  farther  extremities  at 
^  c  d,  pieces  of  phosphorus,  a  very  com- 
bustible  body.  Now,  if  a  lamp  be  placed 
under  the  ball,  it  will  be  found  that  the 
heat  traverses  the  metallic  bars  with  very 
different  degrees  of  facility,  and  the  phos- 
phorus takes  fire  in  very  different  times; 
the  first  that  inflames  is  that  on  the  copper,  then  follows 
that  on  the  brass,  and  a  long  time  after  that  on  the  iron. 
Liquids  are,  for  the  most  part,  very  indifferent  conduct- 
ors of  heat.  This  may  be  established,  for  example,  in  the 
case  of  water,  by  taking  a  glass  jar,  a,  Fig.  278,  nearly 
filled  with  that  substance,  and  introducing  into  it  the  bulb 
of  a  delicate  air-thermometer,  c,  so  that  a  very  short  space 

How  may  it  be  proved  that  different  bodies  conduct  heat  with  different 
degrees  of  facility  ?  How  is  this  affected  by  difference  of  temperature  ? 
Of  the  three  classes  of  bodies  which  conduct  heat  best?.  How  may  dif- 
ference of  conduction  among  metals  be  proved  ? 


CIRCULATION.  255 

intervenes  between  the  top  of  the  bulb  and  the 
surface  of  the  liquid.  If  now  some  sulphuric 
ether  be  placed  on  that  surface,  and  set  on  fire,  it 
will  be  found  that  the  thermometer  remains  mo- 
tionless, aod  we  therefore  infer  that  the  thin 
stratum  intervening  between  the  burning  ether 
and  the  thermometer  cuts  off  the  passage  of  the 
heat.  More  delicate  experiments  have,  however, 
proved  that  the  liquid  condition  is  not,  in  itself,  a 
necessary  obstruction.  Even  water  does  conduct 
to  a  certain  extent;  and  quicksilver,  which  is  equally  a 
liquid,  conducts  very  well. 

But  experience  assures  us  that,  under  common  circum- 
stances, heat  is  uniformly  disseminated  through  liquids 
with  rapidity.  This,  however,  is  due  to  the  establishment 
of  currents  in  their  mass.  We  have  seen  how  readily  this 
class  of  bodies  expands  under  an  elevation  of  tempera- 
ture, and  this  explains  the  nature  of  the  passage  of  heat 
through  them.  When  the  source  of  heat  is  applied  at  the 
bottom  of  a  vessel  containing  water,  those  particles  which 
are  in  immediate  contact  with  the  bottom  become  warm- 
ed by  the  direct  action  of  the  fice,  and  they  therefore  ex- 
pand. This  expansion  makes  them  lighter,  and  they  rise 
through  the  stratum  above,  establishing  a  current  up  to 
the  surface.  Meantime  thetr  place  is  occupied  by  colder 
particles,  which  descend,  and  these  in  their  turn  becom- 
ing warm  follow  the  course  of  the  former.  Circulation, 
therefore,  takes  place  throughout  the  liquid  mass,  in  con- 
sequence of  the  establishment  of  these  currents;  pig.  279. 
and  all  parts  being  successively  brought  in  con- 
tact with  the  hot  surface,  all  are  equally  heat- 
ed. That  these  movements  do  take  place,  may 
be  proved  by  putting  into  a  flask  of  water,  a, 
Fig.  279,  a  number  of  fragments  of  amber, 
adding  a  little  glauber  salt  to  make  their  spe- 
cific gravity  of  the  liquid  more  nearly  that  of 
the  amber,  and  then  applying  a  lamp,  currents 
are  soon  set  up,  and  the  amber,  drifting  in  them, 
marks  out  their  course  in  an  instructive  manner. 

How  may  it  be  proved  that  liquids  are  bad  conductors  of  heat  ?  Is  the 
liquid  state  a  necessary  obstruction  ?  Mention  a  liquid  which  is  a  good 
conductor.  How  is  heat  then  transmitted  through  liquids  ?  On  what  do 
these  currents  depend  ?  How  may  they  be  illustrated  by  means  of  amber  ? 


256  CIRCULATION    IN    GASES. 

Such  currents,  however,  wholly  depend  on  the  point  of 
application  of  the  heat.  If  the  fire,  instead  of  being  ap- 
plied at  the  bottom  of  the  vessel,  is  applied  at  the  top,  as 
in  Fig.  278,  then  the  liquid  can  never  be  warmed.  The 
cause  of  the  movements  of  particles  is  their  becoming 
lighter — they  therefore  float  upward ;  but  if  they  are  al- 
ready situated  on  the  surface  of  course  no  movement  can 
take  place. 

With  respect  to  gases  we  observe  the  same  peculiari- 
ties that  we  do  with  liquids.  Strictly  speaking,  they  are 
Fig.  280.  very  bad  conductors  of  heat;  but  from  the  mo- 
bility of  their  parts,  it  is  very  easy  to  transfer 
heat  readily  through  them,  provided  it  is  right- 
ly applied.  The  experiment  represented  in 
Fig.  280,  shows  how  easily  circulation  takes 
place  in  them.  If  a  piece  of  burning  sulphur 
be  put  in  a  cup,  a,  and  ajar  full  of  oxygen  be 
inverted  over  it,  the  combustion  goes  on  with 
rapidity,  and  the  light  smoke  that  rises  marks 
out  very  well  the  path  of  the  moving  air.  It  rises  direct- 
ly upward  from  the  burning  mass,  until  it  reaches  the  top 
of  the  jar,  and  then  descends  in  circular  wreaths  to  the 
bottom. 

On  the  principle  of  the  difference  of  the  conductibility 
of  bodies,  we  direct  all  our  operations  for  the  communi- 
cation of  heat  with  different  degrees  of  rapidity.  When 
we  desire  to  abstract  the  heat  rapidly  from  bodies,  we 
surround  them  with  good  conductors ;  if  we  wish  to  re- 
tard it,  we  select  such  as  are  bad.  And,  indeed,  it  is  in 
this  way  that  we  regulate  our  changes  of  clothing.  Thick 
woollen  articles,  which  are  very  bad  conductors,  are  adapted 
to  the  cold  winter  weather,  when  we  desire  to  cut  off  the 
escape  of  heat  from  our  bodies  as  much  as  is  in  our  pow- 
er. Nature  also  resorts  to  the  same  principles — the  thick 
coat  of  wool  or  of  hair  which  serves  for  the  covering  of 
animals  protects  them  from  the  cold  by  its  non-conduct- 
ing power.  In  these  instances,  in  reality,  the  action  of 
atmospheric  air  is  brought  into  play,  and  that  under  the 

Why  do  such  currents  depend  on  the  point  of  application  of  the  heat  ? 
Do  the  same  laws  hold  in  the  case  of  gases  ?  How  may  this  be  proved 
by  experiment '(  What  applications  are  made  of  the  principle  of  different 
conductibility  ?  In  the  fur  of  animals  how  is  the  non-conducting  power  of 
air  called  into  use  ? 


POINT   OF   MAXIMUM    DENSITY.  257 

most  favorable  circumstances ;  for  any  motion  of  its  par- 
ticles among  the  thickly  matted  fibres  is  impossible,  and 
its  non-conducting  power,  undisturbed  by  circulation,  is 
rendered  available. 

It  has  been  stated  that  all  bodies  expand  under  the  in- 
fluence of  heat — gases  being  the  most  expansible,  liquids 
next,  and  solids  least.  But  the  expansion  of  the  two  lat- 
ter classes  of  bodies  is  far  irom  beinij  proportional  to 
their  temperature;  for  solids  and  liquids  expand  increas- 
ingly as  their  temperature  rises — one  degree  of  heat,  if 
applied  at  400°,  produces  a  greater  dilatation  than  if  ap- 
plied at  100°.  From  this  irregularity  it  is  believed  that 
gases  are  free — they  seem  to  expand  uniformly  at  all  tem- 
peratures. 

Besides  this  general  irregularity  which  applies  to  all 
solids  and  liquids,  there  are  other  special  irregularities, 
often  of  great  interest.  Water  may  afford  an  example. 
If  some  of  this  liquid  be  taken  at  32°  and  warmed,  in- 
stead of  expanding  it  contracts,  and  continues  to  do  so 
until  it  has  reached  about  39 1°,  after  which  it  expands. 
It  therefore  follows,  that  if  we  take  icater  at  39^°,  whether 
we  warm  it  or  cool  it,  it  expands.  At  that  temperature  it 
is,  therefore,  in  the  smallest  space  into  which  it  can  be 
brought  by  cooling — it  has,  therefore,  the  greatest  densi- 
ty, and  39|°  i&  spoken  of  as  the  point  of  maximum  density 
of  water.  In  the  same  manner  several  other  liquids,  and 
even  solids,  have  points  of  maximum  density. 

This  fact  is  of  considerable  interest,  when  taken  in  con- 
nection with  the  circulatory  movements  we  have  been  de- 
scribing. When  a  mass  of  water  cools  on  a  winter's  night, 
the  colder  particles  do  not  contract  and  descend  to  the 
bottom,  but  after  39|°  is  reached,  they,  being  the  lighter, 
float  on  the  top,  and  hence  freezing  begins  at  the  surface. 
Were  it  otherwise,  and  the  liquid  solidified  from  the  bot- 
tom upward,  all  masses  of  water  during  the  winter  would 
be  converted  into  solid  blocks  of  ice,  instead  of  being 
merely  covered  as  they  are  with  a  screen  of  that  sub- 
stance, which  protects  them  from  further  action. 

Do  solids  and  liquids  expand  with  regularity  ?  Are  there  other  irregu- 
larities besides  this  ?  What  is  meant  by  the  maximum  density  of  water  .' 
At  what  temperature  does  it  take  place  ?  How  does  this  effect  the  freez- 
ing of  masses  of  water  ? 


258  CAPACITY    FOR   HEAT. 


LECTURE  LII. 

CAPACITY  FOR  HEAT  AND  LATENT  HEAT. — Illustration 
of  the  Different  Capacities  of  Bodies  for  Heat. — Stand- 
ards employed. — Process  by  Melting. — Process  of  Mix- 
tures.— Effects  of  Compression. — Effect  of  Dilatation. — 
Latent  Heat. — Caloric  of  Fluidity.— Caloric  of  Elasti- 
city.— Artificial  Cold. 

BY  the  phrase  capacity  of  bodies  for  heat  we  allude  to 
the  fact  that  different  bodies  require  different  degrees  of  heat 
to  warm  them  equally. 

An  experiment  will  serve  to  illustrate  this  important 
fact.  If  we  take  two  bottles  as  precisely  alike  as  we  can 
obtain  them,  and,  having  filled  one  with  water  and  the  other 
with  quicksilver,  set  them  before  the  same  fire,  so  as  to 
receive  equal  quantities  of  heat  in  equal  times,  it  will  be 
found  that  the  water  requires  a  very  much  longer  expos- 
ure, and  therefore  a  larger  quantity  of  heat  than  the  quick- 
silver to  raise  its  temperature  up  to  the  same  point. 

Or  if  we  do  the  converse  of  this,  and  take  the  two  bot- 
tles filled  with  their  respective  liquids,  which,  by  having 
been  immersed  in  a  pan  of  boiling  water,  have  both  been 
brought  to  the  same  degree,  and  let  them  cool  freely  in 
the  air,  it  will  be  found  that  the  water  requires  much 
more  time  than  the  quicksilver  to  come  down  to  the  com- 
mon temperatures.  It  contained  more  heat  at  the  high 
temperature  than  did  the  quicksilver,  and  required  more 
time  to  cool;  it  has,  therefore,  a  greater  capacity  for  heat ; 
or,  to  use  a  loose  expression,  at  the  same  temperature 
holds  more  of  it. 

There  are  several  different  ways  by  which  the  capacity 
of  bodies  for  heat  may  be  determined.  Thus,  we  may 
notice  the  times  they  require  for  warming,  or  those  ex- 
pended in  cooling  in  a  vacuum.  Of  course,  we  cannot 

What  is  meant  by  the  capacity  of  bodies  for  heat  ?  Illustrate  this  by 
experiment.  Can  it  be  proved  conversely?  In  what  ways  may  the  ca'- 
pacity  of  bodies  be  determined  ?  Can  the  absolute  amount  of  heat  in 
bodies  be  determined  ? 


METHOD    OF    MELTING.  259 

tell  the  absolute  amount  of  heat  which  is  contained  in 
any  substance  whatever,  and  these  determinations  are 
hence  relative — different  bodies  being  compared  with  a 
given  one  which  is  taken  as  a  standard.  For  these  pur- 
poses water  is  the  substance  selected  for  solids  and  liquids 
and  atmospheric  air  for  gases  and  vapors. 

An  illustration  will  show  the  methods  by  which  the  ca- 
pacity of  bodies  is  determined  by  the  process  of  melting. 
Let  there  be  provided  a  mass  of  ice,  Fig.  281. 

a  a,  Fig.  281,  in  which  a  cavity,  b  d, 
has  been  previously  made,  and  a  slab 
of  ice,  c  c,  so  as  to  cover  the  cavity 
completely.  In  a  small  flask,  d,  place 
an  ounce  of  water,  raised  to  a  temper- 
ature of  200°.  Set  this  in  the  cavity, 
as  shown  in  the  figure,  and  put  on  the 
slab.  The  ice  now  begins  to  melt ; 
and,  as  the  water  forms,  it  Collects  in  the  bottom  of  the 
cavity.  When  the  temperature  of  the  flask  has  reached 
32°  it  only  remains  to  pour  out  the  water  and  measure 
it.^  Next,  let  there  be  put  in  the  flask  an  ounce  of  quick- 
silver, the  temperature  of  which  is  raised,  as  before,  to 
200° ;  measure  the  water  which  it  can  give  rise  to  by  melt- 
ing the  ice,  precisely  as  in  the  former  experiment,  and  it 
will  be  found  that  the  water  melted  twenty-three  times  as 
much  as  the  quicksilver.  Under  these  circumstances, 
therefore,  a  given  weight  of  water  gives  twenty-three 
times  as  much  heat  as  the  same  quantity  of  quicksilver. 

There  are  still  other  means  of  obtaining  the  same  re- 
sults. Such,  for  instance,  as  by  the  method  of  mixtures. 
If  a  pint  of  water  at  50°  be  mixed  with  a  pint  at  100°  the 
temperature  of  the  mixture  is  75°;  but  it  a  pint  of  mer- 
cury, at  100°,  is  mixed  with  a  pint  of  water,  at  40°,  the 
temperature  of  the  mixture  will  be  60°,  so  that  the  40° 
lost  by  mercury  only  raised  the  water  20°.  That  this 
result  may  correspond  with  the  foregoing,  it  should  be 
recollected  that,  in  this  instance,  we  are  using  equal  vol- 
umes, in  that  equal  weights. 

Why  is  capacity  a  relative  thing  ?  What  is  the  standard  for  solids  and 
liquids  ?  What  is  it  for  gases  and  vapors  ?  Describe  the  process  for  deter- 
mining capacities  by  melting.  How  do  water  and  quicksilver  compare  ? 
Describe  the  process  by  mixtures.  In  ibis,  how  do  water  and  quicksilver 
compare  ? 


260  CHANGES    OF    SPECIFIC    HEAT. 

In  this  way  the  capacities  of  a  great  number  of  bodies 
have  been  determined,  and  tables  constructed  in  which 
they  are  recorded.  Such  tables  are  given  in  the  books 
of  chemistry.  The  different  capacities  of  bodies  are  also 
designated  by  the  term  specific  heat,  since  it  requires  a 
specific  quantity  of  heat  to  heat  bodies  equally. 

When  a  body  is  compressed,  its  specific  heat  or  capaci- 
ty for  heat  diminishes,  and  a  portion  makes  itj  appearance 
as  sensible  heat.  This  may  be  proved  by  rapidly  com- 
pressing air,  which  will  give  out  enough  heat  to  set  tin- 
der on  fire,  or  by  beating  a  piece  of  iron  vigorously,  when 
it  may  be  made  red  hot.  On  the  other  hand,  when  a 
body  is  dilated  its  capacity  for  heat  increases.  It  is  partly 
for  this  reason  that  the  upper  regions  of  the  atmosphere 
are  so  cold  the  specific  heat  is  great  by  reason  of  the  rar- 
ity. It  therefore  requires  a  large  amount  of  heat  to  bring 
the  temperature  up  to  a  given  point. 

It  has  also  been  found  that  the  specific  heat  changes 
with  the  temperature,  increasing  therewith,  so  that  it  is 
not  constant  for  the  same  body. 

There  is  reason  to  believe  that  the  atoms  of  all  simple 
substances  have  an  equal  capacity  for  heat;  and  that 
all  compound  bodies,  composed  of  an  equal  number  of 
single  atoms  combined  in  one  and  the  same  manner, 
have  a  capacity  for  heat  which  is  inversely  as  their  specific 
gravity. 

When  a  solid  substance  passes  into  the  liquid  form  a 
large  quantity  of  heat  is  rendered  latent — that  is  to  say, 
undiscoverable  to  the  thermometer.  Thus,  we  may  have 
ice  at  32°  and  water  at  32°,  the  one  a  solid  and  the  other 
a  liquid,  and  the  precise  reason  of  the  physical  difference 
between  them  is,  that  the  water  contains  about  140°, 
which  the  ice  does  not — a  quantity  which  is  occupied  in 
giving  it  the  liquid  state,  and  is  insensible  to  the  ther- 
mometer. 

For  this  reason  the  transformation  of  a  solid  into  a 
liquid  is  not  an  instantaneous  phenomenon,  but  one  requir- 

What  is  meant  by  specific  heat?  How  does  specific  heat  change  under 
compression  ?  Does  this  take  place  in  solids  as  well  as  gases  ?  What 
reason  is  there  for  the  cold  in  the  upper  regions  of  the  air  ?  Does  spe- 
cific heat  vary  with  the  temperature  ?  What  is  observed  respecting  the 
atoms  of  simple  bodies  ?  What  respecting  compound  ?  What  is  latent 
heat ?  What  is  the  latent  heat  of  water?  Why  does  the  transformation 
of  water  into  ice  or  ice  into  water  require  time  ? 


LATENT  HEAT.  261 

ing  time.  Ice  must  have  its  140°  degrees  oflatent  heat 
before  it  can  turn  into  water.  And,  conversely,  the  solid- 
ification of  a  liquid  is  not  instantaneous.  It  must  have 
time  to  give  out  the  latent  heat  to  which  its  liquid  state 
is  due. 

When  a  liquid  passes  into  the  form  of  a  vapor  it  is  the 
presence  of  a  large  quantity  of  latent  heat  which  gives  to 
it  all  its  peculiarities.  Thus,  water  in  turning  into  steam 
absorbs  nearly  1000°  oflatent  heat,  and  when  that  steam 
reverts  into  the  liquid  state  the  heat  reappears. 

To  the  caloric  which  is  absorbed  during  fusion,  the 
designation  of  caloric  of  fluidity  is  given,  to  that  which 
gives  their  constitution  to  vapors  the  name  of  caloric  of 
elasticity.  And  as  different  bodies  require  during  these 
changes  different  quantities  of  heat,  there  are  furnished 
in  the  works  on  chemistry  tables  of  the  caloric  of  fluidity, 
and  caloric  of  elasticity  of  all  the  more  common  or  im- 
portant bodies.  Of  all  known  bodies  water  has  the 
greatest  capacity  for  heat ;  and,  in  consequence  of  the 
great  amount  of  latent  heat  it  contains,  it  is  one  of  the 
great  reservoirs  of  caloric,  both  for  natural  and  artificial 
purposes. 

Hence,  whenever  a  substance  melts  it  absorbs  heat, 
and  when  it  solidifies  it  gives  out  heat.  When  a  sub- 
stance vaporizes  it  absorbs  heat,  and  when  a  vapor  lique- 
fies it  evolves  heat. 

On  these  principles  depend  some  of  the  processes  re- 
sorted to  for  the  production  of  cold.  If  we  take  two 
solid  bodies,  as  salt  and  snow,  which  have  such  chemical 
relations  to  one  another  that,  when  mixed,  they  produce 
a  forced  fusion  and  enter  on  the  liquid  state ;  before  that 
change  of  form  can  take  place,  caloric  of  fluidity  must  be 
supplied,  for  snow  cannot  turn  into  water  unless  heat  is  giv- 
en it.  The  mixture,  therefore,  abstracting  heat  from  any 
bodies  around  or  in  contact  with  it,  brings  d^wn  their 
temperature  and  thus  produces  cold.  The  same  result 
attends  the  vaporization  of  a  liquid ;  thus,  ether  poured 
on  the  hand  or  on  the  thermometer  produces  a  great 

What  is  the  physical  difference  between  water  and  steam  ?  What  is 
the  caloric  of  fluidity?  What  is  the  caloric  of  elasticity?  What  sub- 
stance has  the  greatest  capacity  for  heat  ?  Why  is  cold  produced  by  a 
mixture  of  salt  and  snow  ?  Why  is  it  produced  by  the  vaporization  of 
ether  ? 


262  PHENOMENA    OF    BOILING. 

cold,  because  the  vapor  which  rises  must  have  caloric  of 
elasticity  in  order  to  assume  its  peculiar  form,  and  it 
takes  heat  from  the  body  from  which  it  is  evaporating  for 
that  purpose. 


LECTURE  LIII. 

ON  EVAPORATION  AND  BOILING. — Phenomena  of  Boiling. 
— Effect  of  the  Nature  of  the  Vessel  and  the  Pressure. — 
Height  of  Mountains  Determined. — Effect  of  Increased 
Pressure.  —  Evaporation. —  Vaporization  in  Vacuo. — 
Effect  of  Temperature  on  a  Liquid  in  Vacuo. — Expla- 
nation of  Boiling. — Nature  of  Vapors. 

As  the  vaporization  of  liquids  is  connected  with  some 
of  the  most  important  mechanical  applications,  we  shall 
proceed  to  consider  it  more  minutely. 

When  water  is  placed  in  an  open  vessel  on  the  fire  the 
temperature  of  the  whole  mass  ascends  on  account  of  the 
currents  described  in  Lecture  LI.  After  a  time  minute 
bubbles  make  their  appearance  on  the  sides  of  the  vessel; 
these  rise  a  little  distance  and  then  disappear,  but  others 
soon  take  their  places,  and  the  water,  being  thrown  into 
a  rapid  vibratory  motion,  emits  a  singing  sound.  Imme- 
diately after  this  the  little  bubbles  make  their  way  to  the 
surface  of  the  liquid,  and  are  followed  by  others  which 
are  larger,  and  the  phenomenon  of  boiling  takes  place. 
The  heat  has  now  reached  212°,  and  it  matters  not  how 
hot  the  fire  may  be,  it  never  rises  higher. 

Different  liquids  have  different  boiling  points,  but  for 
the  same  body,  under  similar  circumstances,  the  point  is 
nearly  fixed.  It  is,  indeed,  in  consequence  of  this  that 
the  boiling  of  water  is  taken  as  the  upper  fixed  point  of 
the  thermometer. 

Of  the  circumstances  which  can  control  the  boiling 
point,  two  may  be  mentioned  :  the  nature  of  the  vessel 
and  the  pressure  of  the  air. 

In  a  polished  vessel,  for  instance,  water  does  not  boil 

Describe  the  different  phenomena  exhibited  during  the  warming  of 
water.  At  what  temperature  does  ebullition  set  in  ?  What  circumstances 
control  the  boiling  point  ?  In  a  polished  vessel  what  is  the  temperature  ? 


EFFECT    OF    PRESSURE.  263 

until  214° ;  but  if  a  few  grains  of  sand  or  other  angular 
body  is  thrown  in 'the  temperature  sinks  to  212°. 

The  absolute  control  which  pressure  exerts  over  the 
boiling  point  may  be  shown  in  many  different 
striking  ways.  Thus,  if  a  glass  of  warm  water 
be  put  under  the  receiver  of  an  air-pump  and 
exhaustion  made,  the  water  enters  into  rapid 
ebullition,  and  continues  boiling  until  its  tem- 
perature goes  down  to  67°.  Water  placed  in 
a  vacuum  will  therefore  boil  with  the  warmth 
of  the  hand. 

Advantage  has  been  taken  of  this  fact  to  determine  the 
height  of  accessible  eminences.  For,  as  we  ascend  in 
the  air,  the  pressure  necessarily  becomes  less;  the  superin- 
cumbent column  of  the  atmosphere  being  shortened,  the 
boiling  point  therefore  declines.  It  has  been  ascertained 
that  if  we  ascend  from  the  ground  through  530  feet,  the 
boiling  point  is  lowered  one  degree ;  and  formulas  are 
given  by  which,  from  a  knowledge  of  that  point,  in  any 
instance  the  altitude  may  be  calculated. 

On  the  other  hand,  when  the  pressure  on  a  liquid  is 
increased,  its  boiling  point  ascends.  This  may  be  proved 
by  taking  a  spherical  boiler,  #,  properly  supported  over 
a  spirit  lamp,  there  being  in  its  top  three  openings  ; 
through  d  let  a  thermometer  dip  into  some  water  which 
half  fills  the  boiler,  at  b  let  there  be  a  stop- 
cock  which  can  be  opened  and  shut  at 
pleasure,  and  through  a  third  opening  be- 
tween these  let  a  tube,  c,  pass,  dipping  down 
nearly  to  the  bottom  of  the  boiler  into  some 
quicksilver  which  is  beneath  the  water. 
Now  let  the  water  boil  freely  and  the  steam 
escape  through  b,  the  thermometer  will 
mark  212°.  Close  the  stop-cock  so  that 
the  steam  cannot  get  out,  but,  being  con- 
fined in  the  boiler,  exerts  a  pressure  on 
the  surface  of  the  water,  which  is  indicated 
by  the  rise  of  the  mercury  in  the  tube.  As  the  column 
rises  the  boiling  point  rises,  and  if  the  instrument  were 

Prove  that  it  is  affected  by  pressure.  At  what  temperature  will  water  boi] 
in  an  air-pump  vacuum  T  How  has  this  been  applied  for  the  determina- 
tion of  heights  ?  How  does  the  boiling  point  vary  when  the  pressure  is 
increased  ? 


264 


MEASURE  OP  ELASTIC  FORCE. 


adapted  to  show  the  results  for  high  pressures,  it  might 
be  proved  that  the  boiling  point 

For  1  atmosphere  is  212°  For  10  atmospheres  is  358.8 

2  "             250.5  15              "               392.8 

3  "             275.2  20              "               418.5 

4  "             293.7  40              «               6665 

5  "             307.5  50             «              690.7 

Besides  this  escape  of  vapor  from  liquids  during  the  act 
of  boiling,  the  same  is  continually  going  on  in  a  slow  and 
motionless  way,  at  lower  temperatures.  If  some  water 
be  left  in  a  shallow  vessel  exposed  to  the  air,  after  a  short 
time  it  all  disappears.  To  this  phenomenon  the  term 
evaporation  is  given. 

At  one  time  it  was  supposed  that  the  atmospheric  air 
acted  on  evaporating  bodies  by  an  affinity  for  their  vapors, 
in  the  same  way  that  a  sponge  will  soak  up  water.  But 
Fig.  284.  the  fallacy  of  this  idea  is  proved  by  the  fact 
that  evaporation  goes  on  more  rapidly  in  vacuo, 
where  no  body  whatever  is  present,  than  in  the 
air.  Thus,  if  into  the  tomcellian  vacuum  of 
a  barometer,  we  pass  a  little  ether,  alcohol,  or 
water,  the  moment  they  reach  the  void  they 
instantly  give  forth  vapor,  and  the  mercurial 
column  is  depressed.  With  ether  the  depres- 
sion is  greatest,  with  alcohol  less,  and  with  wa- 
ter l£ast  of  all.  Now  when  we  consider  the 
nature  of  the  barometer,  and  the  force  which 
keeps  the  column  of  mercury  suspended  in  it, 
it  is  very  clear  that  this  simple  method  affords 


us  an  easy  means  of  knowing  the  elastic  force  of  the  va- 
pors evolved  from  any  of  these  substances  :  for  the  mer- 
curial column  is  depressed  through  the  operation  of  that 
elastic  force.  It  is  this  which  forces  it  downward,  while 
the  pressure  of  the  air  tends  to  force  it  upward. 

By  thus  introducing  liquids  into-  the  barometric  tube, 
we  have  the  means  of  determining  the  elastic  force  of  the 
vapors  to  which  they  give  rise  ;  and  very  simple  exper- 
iments satisfy  us  that  that  elastic  force  depends  upon  the 
the  temperature.  If  we  warm  the  tube,  Fig.  284,  by 

Give  some  examples  of  the  boiling  point  for  different  pressures.  What 
is  meant  by  evaporation  ?  How  can  it  be  proved  that  the  air  does  not  act 
by  its  porosity  like  a  sponge  ?  What  takes  place  when  a  liquid  is  passed 
into  a  torricellian  vacuum  ?  How  can  we  measure  the  elastic  force  of  the 
vapor  evolved  ? 


EFFECT    OF    PRESSURE.  265 

moving  over  it  the  flame  of  a  spirit-lamp,  the  depression 
becomes  greater,  and  if  we  surround  it  by  means   F^.285. 
of  warm  water  in  a  wider  tube,  so  as  to  be  able    r 
to  ascertain  with  accuracy  the  temperature  ap- 
plied, we  shall  discover  that  as  the  heat  rises  the 
elastic  force  of  the  vapor  increases,  and  that  the 
mercurial  column  is  wholly  depressed  into  the  cis- 
tern aft  soon  as  the  temperature  has  reached  the  boil- 
ing point  of  the.  liquid  on  which  ice  are  operating. 

Thus,  let  Abe  a  deep  glass  jar,  filled  to  the  height 
n  with  mercury,  and  let  a  b  be  the  barometric  tube, 
into  the  vacuum  of  which,  at  m,  the  liquid  under 
trial  has  been  passed.  Let  a  wide  tube,  re,  capa- 
ble of  holding  hot  water,  be  adapted,  by  means  of 
a  tight-fitting  cork,  at  s,  to  the  barometric  tube. 
Now  if,  having  observed  the  depression  which  the 
mercury  exhibits  at  common  temperatures,  we  fill 
the  tube,  r  c,  with  hot  water,  a  still  greater  de- 
pression is  the  immediate  result.  The  tempera- 
ture of  the  hot  water,  and,  therefore,  of  the  liquid 
in  the  barometer,  can  easily  be  determined  by 
plunging  a  thermometer  into  the  tube,  r  c. 

From  such  experiments,  therefore,  we  draw  this  im- 
portant conclusion  :  The  elastic  force  of  vapor  rising  from 
a  liquid  at  its  boiling  point  is  equal  to  the  pressure  upon 
it.  If  the  ebullition  be  taking  place  in  the  open  air,  it  is 
therefore  equal  to  the  pressure  of  the  air. 

This  principle  furnishes  a  complete  explanation  of  the 
process  of  boiling,  previously  described.  As  the  temper- 
ature of  a  mass  of  liquid  exposed  to  heat  gradually  rises, 
the  elastic  force  of  the  vapor  it  generates  increases.  Very 
soon,  therefore,  on  the  hottest  part  of  the  vessel,  that  part 
in  immediate  contact  with  the  fire,  the  temperature  reaches 
such  a  point  that  the  vapor  can  form,  the  elastic  force  of 
which  is  just  equal  to  the  atmospheric  pressure.  Little 
bubbles  now  rise  ;  but  these,  having  to  pass  up  through  a 
stratum  above,  which  is  of  a  temperature  somewhat  low- 
er, are  crushed  in  and  disappear.  They  therefore  throw 

Prove  that  that  elastic  force  depends  on  the  temperature.  What  is  the 
elastic  force  when  the  boiling  point  is  reached  ?  What  is  the  elastic  force 
of  a  vapor  when  ebullition  takes  place  in  the  air  ?  How  are  these  princi- 
ples connected  with  the  process  of  boiling  ?  Why  is  a  singing  sound 
emitted  ? 

M 


266 


NATURE    OF    VAPORS. 


vapors. 


the  liquid  into  a  vibratory  motion,  and  cause  the  singing 
sound.  But  soon  the  whole  liquid  attains  such  a  degree 
of  heat  that  the  bubbles  can  make  their  way  to  the  top, 
and  then  bursting,  the  phenomenon  of  ebullition  fairly 
sets  in. 

With  respect  to  the  nature  of  vapors,  there  is  a  good 
Fig.  286.  deal  of  popular  misconception.  Many  persons 
suppose  that  they  are  naturally  of  a  smoky  or 
hazy  aspect.  But  if  we  repeat  the  experiment 
represented  in  Fig.  286,  and  formerly  described 
in  Lecture  VI.,  we  shall  find  that  so  far  as  the 
vapor  of  ether  is  concerned,  it  is  perfectly  trans- 
parent, like  atmospheric  air,  and  by  proper  ex- 
amination the  same  may  be  verified  for  all  other 
The  true  peculiarity  is  the  facility  with  which 
this  form  of  bodies  assumes  the  liquid  state.  The  mo- 
ment the  pressure  of  the  air  is  restored,  in  this  experi- 
ment, the  ethereal  vapor  collapses  into  the  liquid  condi- 
tion. 

The  same  fact  may  be  illustrated  in  another  way.  If 
Fig.  287.  we  take  a  mattrass,  a,  Fig.  287,  and  fill 
the  bulb  and  tube  of  it  with  water,  and 
then  introduce  a  little  sulphuric  ether  into 
its  upper  part,  the  mouth  dipping  beneath 
some  water  contained  in  ajar,  on  heating 
the  bulb  by  a  spirit-larnp  the  ether  pres- 
ently vaporizes.  It  may  now  be  remark- 
ed— 1st.  That  a  vapor  occupies  a  great 
deal  more  space  than  the  liquid  from  which  it  comes  ;  2d. 
That  it  has  not  a  misty  appearance,  but  is  perfectly  trans- 
parent; 3d.  That,  under  a  reduction  of  temperature,  it 
collapses  into  the  liquid  state — for,  on  removing  the  lamp 
and  suffering  the  bulb  to  cool,  the  vapor  disappears. 

Either  by  diminution  of  temperature  or  increase  of 
pressure,  vapors  may  be  condensed  into  the  liquid  state, 
and  in  this  consists  the  chief  distinction  between  them 
and  gases. 

How  can  it  be  proved  that  vapors  are  not  of  a  misty  aspect  ?  What  is 
their  true  peculiarity  ?  What  does  Fig.  287  illustrate?  What  three  facts 
are  proved  by  it  ?  How  may  vapors  be  condensed  into  the  liquid  state  ? 


THE    STEAM    ENGINE. 


267 


LECTURE  LIV. 

THE  STEAM  ENGINE. — Elementary  Steam  Engine. — Forms 
of  this  J\Iachine. — Description  of  the  High-Pressure  En- 
gine.— Principle  of  the  Low-Pressure  Engine." — De- 
scription of  the  Double- Acting  Engine. — Estimate  of 
Performance. 

ON  the  elastic  force  of  steam  and  on  the  rapidity  with 
which  it  is  condensed  by  application  of  cold,  the  construc- 
tion of  the  different  forms  of  steam  engine  depends. 

The  instrument  represented  in  Fig.  288  Fig-  28& 
gives  a  clear  idea  of  the  elementary  parts 
of  a  steam  engine.  It  consists  of  a  cylin- 
drical glass  tube,  B,  terminating  in  a  bulb, 
A.  In  the  tube  a  piston  moves  up  and 
down,  air-tight,  and  a  little  water  having 
been  placed  in  the  bulb,  it  is  brought  to  the 
boiling  point  by  the  application  of  a  lamp. 
As  the  steam  forms  it  presses  the  piston  up- 
ward by  reason  of  its  elastic  force,  and  on 
dipping  the  bulb  into  cold  water  the  steam 
condenses,  and  produces  a  partial  vacuum, 
the  piston  being  driven  downward  by  the 
pressure  of  the  air. 

There  are  a  great  many  modifications  of 
the  steam  engine.  They  may,  however,  for  the  most  part, 
be  reduced  to  two  kinds:  1st,  high-pressure  engines;  2d, 
low-pressure  engines. 

The  high-pressure  engine,  which  is  the  simplest  of  the 
two  forms,  consists  essentially  of  a  very  strong  iron  ves- 
sel or  boiler,  in  which  the  steam  is  generated,  a  cylinder, 
in  which  a  steam-tight  piston  moves  backward  and  for- 
ward, an  arrangement  of  valves  or  cocks,  so  adjusted  as 
alternately  to  admit  the  steam  above  and  below  the  pis- 
ton, and  also  alternately  to  let  it  escape  into  the  air; 

On  what  two  principles  do  the  different  kinds  of  steam  engine  depend  ? 
Describe  the  instrument  represented  in  Fig.  288.  What  are  the  chief 
varieties  of  the  steam  engine  ?  Describe  the  high-pressure  engine. 


268 


HIGH-PRESSURE    ENGINE. 


and  lastly,  a  suitable  contrivance  by  which  the  oscilla- 
tions of  the  piston  may  be  converted  into  other  kinds  of 
motion,  suited  to  the  work  which  the  engine  has  to  per- 
form. 

The  action  of  the  steaminoneof  these  machines  may  be 
Fig.  289.  understood  from  the  annexed  diagram,  Fig.  289. 
Let  f  be  the  cylinder,  in  which  a  solid  piston,  e, 
moves,  steam-tight,  and  let  us  suppose  the  piston 
near  to  the  bottom  of  the  cylinder.  The  steam 
,  is  now  admitted  through  an  aperture,  a,  and  by 
its  elastic  force  pushes  the  piston  to  the  top  of 
the  cylinder.  The  movement  of  the  piston-rod 
rearranges  the  openings  into  the  cylinder,  clos- 
ing at  a  particular  moment  # ,  through  which  the 
steam  has  already  come,  and  opening  b;  simul- 
taneously, also,  it  opens  c  and  closes  d.  Through 
c,  from  the  boiler,  a  fresh  supply  of  steam  ar- 
rives, while  it  is  shut  off  from  a.  This  steam 
cannot  escape  through  d,  because  that  is  closed 
— it  therefore  takes  effect  upon  the  piston  and 
pushes  it  downward,  all  the  vapor  beneath  es- 
caping out  into  the  air  through  b,  which  has 
been  opened.  This  downward  move'ment  of 
the  piston-rod  rearranges  all  the  valves,  reversing  the  po- 
sitions they  have  jusf  had.  It  therefore  opens  a,  shuts  b, 
opens  d,  and  shuts  c.  Steam  now  comes  in  from  the 
boiler,  through  <z,  but  cannot  escape  through  b  ;  it  there- 
fore pushes  up  the  piston,  driving  out  the  steam,  which  is 
on  its  opposite  side,  through  d,  and  in  this  way  a  recip- 
rocating motion  is  produced. 

The  means  of  opening  and  shutting  the  apertures  lead- 
ing into  the  cylinder  at  the  proper  moment  differ  in  dif- 
ferent engines — sometimes  cocks  are  used,  and  sometimes 
sliding  valves. 

In  this  engine,  therefore,  the  piston  moves  in  both  ways 
against  the  pressure  of  the  air.  The  steam  must  be  ne- 
cessarily raised  from  water  at  a  high  boiling  point,  and 
hence  these  machines  are  much  more  liable  to  accident 
than  the  low-pressure  engine,  now  to  be  described. 

The   rapid    condensibility  of  steam — a   principle  inti- 

Describe  the  circumstances  under  which  the  steam  is  alternately  ad- 
mitted above  and  below  the  piston.  How  are  the  necessary  apertures 
opened  and  closed  ?  Why  must  the  steam  be  raised  at  high  pressure  1 


a 


CONDENSIBILITY    OF    STEAM. 


269 


mately  concerned  in  the  action  of  the  low-pressure  en- 
gine— may  be  illustrated  in  the  fol-  2^.290. 
lowing  manner:  Take  a  glass  flask,  a, 
Fig.  290,  and  adjust  to  its  mouth  a 
wide  bent  tube,  b,  both  ends  of  which 
are  open,  having  previously  placed  a 
quantity  of  water  in  the  flask.  Apply 
the  flame  of  a  spirit-lamp,  and  bring 
the  water  to  the  boiling  point,  contin- 
uing the  ebullition  until  all  the  air  is 
driven  out  of  the  flask,  and  nothing 
but  steam  remains.  Then  dip  the  open 
end  of  the  tube  into  the  jar,  c,  containing  some  cold  wa- 
ter, and  remove  the  lamp ;  the  steam  in  the  tube  will  at 
once  begin  to  condense,  through  the  influence  of  the  cold 
water,  which  soon  rises  over  the  bent  portion  and  precip- 
itates itself  into  the  flask,  often  with  so  much  violence  as 
to  break  it  to  pieces. 

Of  the  low-pressure  engine  we  have  varieties — such  as 
the  single-acting  and  the  double-acting  engine.  In  the 
former,  the  piston  is  driven  one  way  by  means  of  steam 
acting  against  a  vacuum,  returning  the  other  way  by  the 
counterpoising  weight  of  the  machinery.  The  machine, 
therefore,  in  reality,  is  only  in  action  during  half  its  mo- 
tion. 

The  double-acting  engine  has  the  steam  employed  to 
produce  both  the  ascent  and  descent  of  the  piston  into  a 
vacuum  on  the  opposite  side.  It  therefore  works  contin- 
uously. 

In  expansive  engines  the  supply  of  steam,  instead  of 
being  continued  during  the  entire  ascent  or  descent  of 
the  piston,  is  cut  off  when  the  movement  is  one  half  or 
one  third  accomplished.  The  expansion  of  that  steam 
driving  the  piston  through  the  rest  of  the  cylinder. 

The  following  is  a  description  of  the  double-acting  en- 
gine :  Fig.  291  represents  the  boiler  and  its  appurtenances, 
Fig.  292  the  engine. 

B  B,  Fig.  291,  is  the  boiler,  of  a  cylindrical  shape,  the 
fire,  F  F,  is  applied  beneath,  W  W  is  the  water-level, 
and  S  is  occupied  by  steam.  At  tt  there  is  a  bent  glass 

Give  an  illustration  of  the  instantaneous  condensation  of  steam.  What 
is  the  nature  of  the  single-acting  steam  engine  ?  What  is  meant  by  the 
expansive  engine  ?  What  is  the  double-acting  engine  ? 


270 


STEAM-BOILER. 


tube,  open  at  both  extremities,  and  so  arranged  that  one 
end  is  in  the  steam-space,  and  the  other  in  the  water; 


Fig.  291. 


it  serves  to  show  the  level  of  the  water  in  the  boiler.  In 
some  cases,  two  cocks,  c  and  d,  are  inserted  in  the  boiler, 
one  entering  into  the  steam  part  and  one  beneath  the 
water.  On  opening  them,  if  the  water  is  at  its  proper 
level,  steam  will  escape  from  the  upper  and  water  from 
the  under  one.  If  there  is  too  much  water,  it  escapes 
from  both  ;  if  two  little,  steam  escapes  from  both.  The 
boiler  is  continually  replenished  by  the  feed-pipe,  the  na- 
ture of  which  has  been  explained  in  Lecture  XIV.  At 
M  there  is  a  barometer-gauge,  to  show  the  elastic  force 
of  the  steam ;  at  e  a  b  a  safety-valve,  with  its  weight,  w  ; 
this  opens  upward,  so  that,  should  the  elastic  force  in  the 
interior  of  the  boiler  become  too  great,  the  valve  opens, 
and  the  steam  escapes.  On  the  contrary,  to  prevent  the 
boiler  being  crushed  in  by  the  atmospheric  pressure, 
when  the  expansive  force  of  the  steam  happens  to  de- 
cline, there  is  a  second  valve  at  U,  with  its  lever,  a  c  b, 

Describe  the  principal  parts  of  its  boiler.    What  are  the  two  safety- 
valves  ? 


DOUBLE-ACTING    ENGINE. 


271 


and  weight,  w,  which  opens  inward,  that,  when  the  ex- 
ternal pressure  exceeds  the  weight,  the  air  may  find  ac- 
cess to  the  inside  of  the  boiler.  And,  as  it  is  necessary 
from  time  to  time  to  clear  the  boiler  from  the  incrusta- 
tions or  deposits  of  salt  and  other  impurities,  there  is  an 
opening,  as  at  L,  through  which  access  can  be  had. 
This,  of  course,  is,  at  other  times,  securely  closed.  Last- 
ly, from  the  boiler  there  passes  the  steam-pipe,  s,  which 
is  opened  by  the  valve  at  N. 

Fig.  292  represents  the  engine,  properly  speaking.  At 

Fur.  292. 


z  z  it  should  be  imagined  as  being  continuous  with  z  z 
of  Fig.  291,  so  that  in  both  figures  the  tubes  i  i  and  s  s 
are  continuous.  In  both  s  is  the  tube  along  which  the 
steam  from  the  boiler  is  delivered  to  the  cylinder.  Pass- 
ing through  the  four -way  cock,  a,  either  down  through  a 
or  up  through  b,  into  the  cylinder  C,  in  which  the  piston, 
P,  moves.  Admission  for  the  steam,  above  or  below  the 
piston,  is  regulated  by  a  system  of  levers,  y  y,  the  neces- 
sary motion  being  communicated  by  the  machine  itself. 


Describe  the  principal  parts  of  the  engine, 
hen  it  leaves  the  cylinder  ? 


What  becomes  of  the  steam 


272  HYGROMETRY. 

The  piston-rod,  E,  is  connected  with  the  beam,  B  F, 
working  on  the  fulcrum,  A.  The  connecting-rod  is  F  R. 
At  R  itfis  attached  to  the  crank  by  a  pivot,  H  H  H,  being 
the  fly-wheel,  the  revolution  of  which  gives  uniformity  to 
the  motion.  The  steam,  after  elevating  or  depressing 
the  piston,  passes  through  the  eduction-pipe,  ff,  into  the 
condenser,  J,  which  is  immersed  in  a  cistern,  L,  of  cold 
water.  In  this  it  is  condensed  into  water  by  a  jet  which 
passes  through  the  injection-cock.  The  resulting  warm 
water  is  pumped  out  by  the  air-pump,  O,  into  the  hot 
well,  W ;  thence  it  is  carried,  by  the  hot-water  pump,  Z», 
along  the  feed-pipe,  i  i,  into  the  boiler.  The  cold-water 
pump,  S,  supplies  the  reservoir  with  cold  water.  All  the 
pumps  are  worked  by  the  beam  of  the  engine.  The  sup- 
ply of  steam  is  regulated  by  the  governor,  G,  so  as  to  be 
kept  constant. 

The  performance  of  steam  engines  is  commonly  esti- 
mated by  horse-power.  The  value  of  the  power  of  one 
horse  is  a  force  sufficient  to  raise  33,000  pounds  one  foot 
high  in  one  minute. 


LECTURE  LV. 

HYGROMETRY,  OR  THE  MEASUREMENT  OF  THE  QUANTITY 
OF  VAPOR. —  Hygrometers. — Sponge  and  Paper  Hy- 
grometers.—  Saussure's  Hair  Hygrometer. —  Mode  of 
Graduating  it. —  The  Dew  Point. —  Process  for  the 
Dew  Point. — Daniel's  Hygrometer. —  The  Psychrome- 
ter. — Process  for  Drying  Gas. 

FOR  many  scientific  purposes  it  is  often  necessary  to 
determine  the  amount  of  vapor  of  water  in  the  air  or  in 
various  gases.  We  have  already  observed,  Lecture  III, 
that  the  quantity  of  moisture  in  the  atmosphere  is  con- 
stantly changing ;  and  this  is  connected  with  a  great  num- 
ber of  interesting  meteorological  phenomena. 

Instruments  have  been  invented  with  a  view  of  giving 
indications  of  the  relative  degrees  of  dampness  of  the  air. 

What  is  done  with  the  resulting  hot  water?  How  are  the  movements 
of  the  different  pumps  and  valves  accomplished  ?  What  is  the  value  of  a 
horse-power  ? 


SPONGE    HYGROMETER. 


273 


They  have  received  the  names  of  hygroscopes  and  hy- 
grometers. 

A  great  many  organic  substances  change  their  dimen- 
sions according  as  they  are  exposed  to  various  degrees 
of  moisture,  expanding  or  contracting.  Among  such  may 
be  mentioned  ivory,  hair,  whalebone,  wood,  &c.  Any  of 
these  connected  with  a  mechanism,  by  which  the  change 
of  volume  might  be  registered,  would  furnish  a  hygrom- 
eter. They  all,  however,  lose  their  sensitiveness  in  the 
course  of  time.  Thus,  it  is  well  known  that  wood,  when 
it  is  seasoned,  is  much  less  liable  to  these  changes  than 
when  it  is  in  a  recent  state. 

There  are  other  bodies,  among  which  might  be  enu- 
merated many  salts,  which,  by  absorbing  moisture  from 
the  air  increase  in  weight,  and  by  returning  it  back  again, 
become  lighter.  Most  of  the  powerful  acids,  as  the 
sulphuric,  also  the  alkalies,  as  potash  and  soda,  possess 
an  intense  affinity  for  water.  Advantage  has  been  taken 
of  this  property  in  the  construction  of  hygrometers,  by 
attaching  a  sponge,  soaked  in  weak  pearlash,  to  one  arm 
of  a  balance,  the  index  of  which  plays  over  a  graduated 
scale,  and  shows  the  influence  of  the  existing  moisture 
by  the  sponge  becoming  heavier  or  lighter.  For  such 


.  293. 


contrivances  paper  is  a  very  suitable  substance.  Thus, 
let  G  G,  Fig  23Q,  be  a  case,  the  front  of  which  is  of  glass 
and  the  sides  of  gauze  or  some  other  material,  pervious 
to  the  air;  let  D  be  the  beam  of  a  light  balance  suspend- 

What  are  hygroscopes  or  hygrometers  ?     Mention  some  bodies  which 
change  under  the  influence  of  moisture.     Describe  the  sponge  hygrometer. 


274 


PAPER    HYGROMETER. 


ed  within,  working  on  the  fulcrum  g,  and  supported  by 
two  brackets,  A  A.  From  the  beam  let  there  pass  an  index, 

Fig.  294. 


E,  which  moves  over  a  scale,  C,  graduated  into  100  equal 
parts,  and  suspended  on  a  support,  B.  From  one  end 
of  the  beam  let  there  hang  the  hygroscopic  body,  I, 
which  consists  of  a  great  number  of  round  pieces  of  thin 
paper,  fastened  together  by  three  or  more  threads,  form- 
ing a  column,  with  spaces  between  each  of  the  parallel 
pieces-  of  paper,  that  the  air  may  have  complete  access  to 
the  whole  mass.  This  hygroscopic  body  is  properly  coun- 
poised  by  a  weight,  H,  in  the  opposite  scale-pan.  At  F 
there  is  a  button,  which  slides  upon  the  index ;  it  is  to 
be  arranged  in  such  a  position  that  a  weight  of  one  grain 
put  on  the  top  of  the  hygroscopic  body  will  drive  the 
index  from  0  to  100  exactly.  The  papers  are  now  to  be 
thoroughly  dried,  by  placing  a  dish  of  sulphuric  acid  in 
the  case,  or  in  any  other  suitable  manner ;  and  when  that 
is  accomplished,  weights  are  to  be  added  at  H  to  bring 
the  index  to  0.  When,  now,  it  is  exposed  to  the  air,  the 
papers  become  heavier,  and  the  index  plays  over  the 
scale.  The  instrument,  therefore,  acts  from  the  dry  ex- 
treme;  but,  though  its  movements  are  interesting,  for  it 
is  constantly  traversing,  it  is  devoid  of  exactitude. 

The  hair  hygrometer  of  Saussure  is  more  simple  and 
effectual.     It  consists   of  a  human  hair  8  or  10  inches 


Describe  the  hygrometer  represented  in  Fig.  2C 
does  this  instrument  act? 


From  what  extreme 


SAUSSURE  S    HYGROMETER.  275 

long,  b  c,  Fig.  295,  fastened  at  one  extremity  to  a  screw, 
a,  and  at  the  other  passing  over  a  pulley,  c, 
being  strained  tight  by  a  silk  thread  and  weight,  F*8' 295' 
d.  From  the  pulley  there  goes  an  index  which 
plays  over  the  graduated  scale  e  e',  so  that, 
as  the  pulley  turns  through  the  shortening  or 
lengthening  of  the  hair,  the  index  moves.  The 
instrument  is  graduated  to  correspond  with 
others  by  first  placing  it  under  a  bell  jar  along 
with  a  dish  of  sulphuric  acid,  caustic  potash, 
chloride  of  calcium,  or  other  substance  having 
an  intense  affinity  for  water,  this  absorbs  all  the 
moisture  of  the  air  in  the  bell,  and  brings  it  to 


absolute  dryness.  The  hair,  therefore,  contracts  and 
moves  the  pulley  and  its  index.  When  this  contraction  is 
complete,  the  point  at  which  the  index  stands  is  marked  0. 
The  hygrometer  is  then  placed  under  a  jar,  the  interior 
of  which  is  thoroughly  moistened  with  water  and  set  in  a 
vessel  with  that  liquid,  so  as  to  bring  the  included  air  to 
a  condition  saturated  with  moisture.  The  index  moves, 
and  when  it  has  become  stationary  the  point  opposite  to 
which  it  stands  is  marked  100°.  The  intervening  space 
is  then  divided  into  100  equal  parts,  and  the  instrument 
is  complete. 

It  is  to  be  observed  that  the  hair  requires  some  pre- 
vious preparation  to  give  it  its  full  hygrometric  sensibility  ; 
this  is  accomplished  by  removing  from  it  all  oily  matter 
by  soaking  it  in  a  weak  solution  of  potash. 

As  respects  the  nature  of  the  indications  of  this  instru- 
ment, it  is  to  be  understood,  that  it  by  no  means  follows 
that,  when  the  index  stands  at  25  or  50,  the  air  contains 
one  quarter  or  one  half  the  moisture  it  does  at  100. 
Tables  have,  however,  been  constructed,  which  exhibit 
the  value  of  its  degrees. 

A  much  more  exact  method  is  that  known  as  the  pro- 
cess for  tlie  daw  point.  In  practice  it  is  very  simple,  and 
may  be  thus  described.  If  we  take  a  glass  of  water,  and, 
by  putting  in  it  pieces  of  ice,  cool  it  down,  after  a  time 
moisture  will  begin  to  dim  the  outside.  If  a  thermometer 

Describe  the  hair  hygrometer  of  Saussure.  How  are  its  two  fixed  points 
of  absolute  dryness  and  maximum  moisture  found  '(  What  previous  prep- 
aration does  the  hair  require?  What  is  to  be  observed  as  respects  its 
indications  ? 


276 


DANIELS    HYGROMETER. 


is  immersed  in  the  water  we  may  determine  the  precise 
degree  at  which  this  deposit  takes  place;  and,  knowing 
the  temperature  of  the  external  air  for  the  time  being, 
we  can  tell  the  number  of  degrees  through  which  it,  must 
be  cooled  before  the  dew  point  (or  the  point  at  which 
moisture  deposits)  is  reached.  Now,  when  the  air  is 
very  moist  it  is  necessary  to  cool  it  very  little  before  this 
effect  ensues  j  but  when  it  is  dry  the  cooling  must  be 
carried  to  a  correspondingly  lower  degree.  If  the  air 
were  perfectly  saturated  the  slightest  depression  of  tem- 
perature would  make  the  moisture  precipitate.  Know- 
ing, therefore,  the  dew  point,  the  barometric  pressure, 
and  the  existing  temperature,  if  it  is  required  to  find  the 
actual  quantity  of  moisture  in  the  air  it  can  be  determined 
by  calculation. 

Daniel's   hygrometer  is   a  very   beautiful  instrument 


-  296. 


for  determining  the  dew 
point.  It  consists  of  a 
bent  tube,  a  c  b,  Fig. 
296,  at  the  extremities 
of  which  two  bulbs,  a  b, 
are  blown  ;  b  is  made  of 
black  glass  and  a  is  cov- 
ered over  with  a  piece 
of  muslin.  The  bulb  b  is 
half  full  of  ether,  and  the 
instrument  -maker  con- 
trives things  so  that  the 
rest  of  the  tube  is  void 
of  air,  and  contains  the 
vapor  of  ether  only.  A 
delicate  thermometer,  d, 
has  its  bulb  dipping  into 
the  ether  of  b.  There  is 
also  another  thermometer  attached  to  the  stem  of  the 
instrument.  Under  these  circumstances,  if  the  muslin 
cover  of  a  is  moistened  with  a  little  ether,  that  bulb 
becomes  at  once  cooled  by  the  evaporation,  the  vapor 
within  it  condenses  and  a  fresh  quantity  distils  over  from 
b  to  supply  its  place.  But  b  cannot  furnish  the  vapor 
without  its  own  temperature  descending,  for  latent  heat, 

Describe  the  process  for  the  dew  point.     What  is  Daniel's  hygrometer  ? 
How  is  this  instrument  used  ? 


THE    PSYCHROMETER.  277 

is  required  before  the  vapor  can  form.  After  a  time, 
therefore,  through  the  cooling  agency  dew  begins  to 
deposit  on  the  black  glass,  and  the  point  at  which  this 
takes  place  is  determined  by  the  included  thermometer. 

The  psyckrometer  consists  of  two  delicate  mercurial 
thermometers  divided  into  fractions  of  degrees,  and  cor- 
responding perfectly  with  one  another.  The  bulb  of  one  of 
them,  A,  Fig.  297,  is  covered  with  muslin,  that  of  the  other, 
B,  is  left  naked.  On  the  central  pillar  there  is  arranged 
a  reservoir,  W,  of  distilled  water,  from  which  a  thread 
passes  to  the  muslin  of  A,  and  keeps  it  constantly  moist, 
as  the  water  evaporates  from  this  bulb  the  mercury 
begins  to  fall,  and  the  drier  the  air  the  greater  the  de- 
scent. As  soon  as  the  air  round  the  bulb  is 
saturated  with  moisture  the  point  at  which 
the  mercury  stands  is  the  dew  point.  If 
both  thermometers,  the  damp  and  the  dry, 
coincide,  the  air  contains  moisture  at  its  20, 
maximum  density,  and  the  greater  the  dif- 
ference between  them  the  dryer  the  air. 

For  many  purposes  in  chemistry  and  phy- 
sical  science   it  is  necessary  to  remove  all 
moisture    from    atmospheric    air    and   from 
gases.     This   may  be  done    by   conducting 
them  through  tubes  containing  bodies  which 
have  a  strong  attraction  for  water.     The  bodies   com- 
monly  selected    for   this    purpose  Fig.  298. 
are  chloride  of  calcium,  hydrate  of 
potash,  phosphoric  acid,  and  frag- 
ments of  glass  or  quartz  moistened 
with  oil  of  vitriol.     The  process  is 
as  represented  in  Fig.  298,  where 
a  is  the  flask  from  which  the  gas  to 
be  dried  is  evolved,  b  a  bent  tube 
which  conducts  it  into  a  wider  tube,  c,  containing  the 
absorbent  material.     It  escapes  from  d  in  a  dry  state. 

Describe  the  psychrometer.  Why  does  one  thermometer  commonly 
stand  lower  than  the  other  ?  What  substances  are  used  in  chemistry  as 
drying  agents  ?  How  are  they  employed  ? 


278  MAGNETISM. 


MAGNETISM. 


LECTURE  LVI. 

MAGNETISM. —  The  Loadstone. — Artificial  Magnets. — Po- 
larity.—  Transmission  of  Effect. —  The  Poles  and  Axis. 
— Magnetic  Curves. — Law  of  Attraction  and  Repulsion. 
—  Transient  Magnetism  of  Iron.  —  Permanent  Magnet- 
ism of  Steel. — Induced  Magnetism. — Law  of  Diminu- 
tion.— Simultaneous  Existence  of  Polarities. — Processes 
for  Imparting  Magnetism. 

MANY  centuries  ago  it  was  discovered  that  a  certain 
ore  of  iron,  which  now  passes  under  the  name  of  the  mag- 
net or  loadstone,  possesses  the  remarkable  quality  of  at- 
tracting pieces  of  iron.  Subsequently  it  was  found  that 
the  same  power  could  be  communicated  to  bars  of  steel, 
by  methods  to  be  described  hereafter. 
Fig.  299.  Bars  of  steel  so  prepared  pass  under  the  name 
of  artificial  magnets,  to  distinguish  them  from  the 
natural  loadstone.  When  they  are  of  small  size 
they  are  commonly  called  needles.  A  magnetic 
bar  bent  into  the  shape  represented  in  Fig.  299, 
is  called  a  horse-shoe  Fig.  soo. 

magnet,  and  several 
magnets  applied  to-  g. 
gether  take  the  name 
of  compound  magnets,  or  a 
bundle  of  magnets.' 

The  Chinese  discovered 
that  when  a  magnetic  needle 
is  poised  on  a  pivot,  as  in 

What  is  the  magnet  or  loadstone  ?   What  are  artificial  magnets  ?  What 
are  needles ''.     What  is  a  horse  shoe  magnet  ? 


MAGNETIC    POLES. 


279 


Fig.  300,  or  floated  on  water  by  a  piece  of  cork,  that  it 
spontaneously  takes  a  direction  north  and  south ;  and  if 
purposely  disturbed  from  that  position  it  returns  to  it 
again  after  a  few  oscillations. 

By  a  needle  so  suspended,  the  fundamental  fact  of  the 
attraction  of  the  magnet  for  iron  is  easily  verified.  Pre- 
sent a  mass  of  iron  to  either  extremity  of  the  needle,  and 
the  needle  instantly  moves  to  meet  it. 

If  a  bar  magnet  is  brought  near  a  nail  or  a  mass  of 
iron-filings,  the  iron  will  be  suspended. 

That  these  effects  take  place  through  glass,  paper,  and 
solid  and  liquid  substances  generally,  may  be  thus  estab- 
lished. A  quantity  of  iron-filings  being  laid  on  a  pane  of 
glass,  if  a  magnet  be  approached  beneath,  the  filings  fol- 
low its  motions.  But  if  a  plate  of  iron  intervenes  the 
magnetic  influence  is  almost  wholly  cut  off. 

The  power  of  a  magnetic  bar  is  not  equal  in  all  parts. 
There  is  a  point  .situated  near  each  end,  which  seems 
to  be  the  focus  of  action.  To  these  points  the  names  of 
poles  are  given,  and  the  line  joining  them  is  called  the 
axis. 

If  a  bar  magnet  be  rolled  in 
iron-filings,  they  attach  them- 
selves for  the  most  part  at  the 
two  poles,  d  dj  Fig.  301  :  or, 
if  such  a  bar  be  placed  under 
the  surface  of  which 
filings  are  dusted, 


Fig.  301 


sheet  of  pasteboard,  on 

Fig.  302. 


are 

they  arrange  them- 
selves in  curved  lines, 
as  shown  in  Fig.  302, 
which  are  symmetri- 
cally situated  as  re- 
spects the  poles,  P  P. 
When  a  magnet  is 
freely  suspended  it 
arranges  itself  north 
and  south,  as  has  been  stated.  To  that  pole  which  is  to- 

How  may  the  polarity  of  a  needle  be  shown  ?  How  may  its  attraction 
for  iron  be  shown  ?  Prove  that  these  effects  take  place  through  glass,  but 
not  through  iron.  Is  the  magnetic  power  equally  diffused  through  a  bar? 
What  are  the  poles  ?  What  is  the  axis  ?  How  may  it  be  proved  that  the 
poles  are  the  foci  of  action  ?  How  may  the  magnetic  curves  be  exhibited? 


280  ATTRACTION    AND    REPULSION. 

ward  the  north  the  name  of  north  pole  is  given,  the  other 
is  the  south  pole. 

When,  instead  of  presenting  to  a  suspended  needle  a 
piece  of  iron,  we  present  to  it  another  magnet,  phenom- 
ena of  repulsion  as  well  of  attraction  ensue — if  the  north 
pole  of  one  be  presented  to  the  north  of  the  other,  repul- 
sion takes  place,  and  the  same  occurs  if  two  south  poles 
are  presented.  But  if  it  be  a  north  and  a  south  pole  then 
attraction  takes  place. 

These  results  may  be  grouped  together  under  the  sim- 
ple law — "  Like  poles  repel  and  unlike  ones  attract." 

There  is,  therefore,  an  antagonization  of  effect  between 
opposite  magnetic  poles.  If  a  key  be  suspended  to  a 
magnet  by  its  north  pole,  on  the  approach  of  the  south 
pole  of  one  of  equal  force  the  key  drops  off. 

If  we  examine  the  force  of  a  magnet,  commencing  at 
either  of  its  poles  and  going  toward  its  center,  the  in- 
tensity gradually  declines.  It  ceases  altogether  about 
midway  between  the  poles.  This  point  is  termed  the 
point  or  line  of  magnetic  indifference. 

Magnetism  may  be  excited  in  both  iron  and  steel ;  in 
the  former  with  greater  rapidity,  in  the  latter  more  slow- 
ly. The  magnetism  which  soft  iron  has  received  it  in- 
stantly loses  on  being  removed  from  the  source  which  has 
given  it  magnetism  ;  but  steel  retains  its  virtue  perma- 
nently. Soft  iron  is,  therefore,  transiently — hard  steel 
permanently  magnetic. 

When  a  mass  of  iron  is  in  contact  with  the  pole  of  a 
magnet,  it  obtains  the  same  kind  of  magnetism  as  the  pole 
with  which  it  is  in  contact  throughout  its  whole  mass,  and 
can,  in  the  same  manner,  communicate  a  similar  quality 
to  a  second  mass  brought  in  contact  with  it;  and  this  to 
a  third,  arid  so  on.  Thus,  if  from  the  pole  of  a  magnet  a 
key  be  suspended,  this  will  suspend  a  second,  and  that  a 
third,  &c.,  until  the  weight  becomes  too  great  for  the  mag- 
net to  hold.  If,  having  two  or  three  keys  thus  suspend- 
ed, we  take  hold  of  the  uppermost  and  gently  slide  away 
the  magnet,  the  moment  it  is  removed  the  keys  all  fall 
apart,  showing  the  sudden  loss  of  power  in  soft  iron. 

What  is  the  general  law  of  magnetic  attractions  and  repulsions  ?  How 
does  the  intensity  vary  in  a  magnet  ?  When  is  the  point  of  magnetic  in- 
difference ?  What  is  the  difference  between  the  magnetism  of  steel  and 
of  iron  ?  Illustrate  the  communication  of  magnetism. 


MAGNETIC    POLARITY.  281 

But  a  mass  of  iron  can  receive  magnetism  at  a  distance 
from  the  magnet  itself.  To  this  phenomenon  the  FJ^.  303. 
name  of  induction  is  given,  and  the  distance  through 
which  this-  effect  can  take  place  is  called  the  mag- 
netic atmosphere.  The  general  effect  of  induction 
may  be  exhibited  by  bringing  a  powerful  magnet 
near  a  large  key,  as  in  Fig.  303,  when  it  will  be 
found  that  the  large  key  will  support  smaller  ones; 
but  as  soon  as  it  is  removed  from  the  influence  of 
the  magnet  these  all  drop  off. 

When  magnetism  is  thus  induced  by  the  action  of  a 
given  pole,  that  end  of  the  disturbed  body  which  is  near- 
est to  the  pole  has  an  opposite  polarity  ;  but  the  farther 
end  has  the  same  polarity  as  the  disturbing  pole. 

The  force  of  magnetic  action  varies  with  the  distance. 
It  has  been  proved  by  Coulomb  and  others,  that  the  in- 
tensity of  magnetic  action  is  inversely  proportional  to  the 
square  of  the  distance.  At  twice  a  given  distance  it  is, 
therefore,  one  fourth,  at  three  times  One  ninth,  &c. 

Both  magnetic  polarities  must  always  simultaneously 
occur.  We  can  never  have  north  magnetism  or  south 
magnetism  alone.  Thus,  Fig.  304. 

if  we  take  a  long  mag-      T& s 

net,  N  S,  Fig.  304,  and        f  I 

break  it  in  two,  we  shall      ,  ,      ^  g// 

not   insulate    the   north     , k        r j 

polarity  in  one  half  and     I— — — — — 
the  south  in  the  other,  but  each  of  the  broken  magnets 
will  be  perfect,  in  itself,  having  two  poles — one  fragment 
being  N'  S'.arid  the  other  N"  S". 

When  the  poles  of  a  magnet  are  polished,  and  covered 
with  smooth  plates  of  iron,  the  magnet  is  said  to  be  armed. 
The  piece  of  soft  iron  which  passes  from  pole  to  pole  of 
a  horse-shoe  magnet  is  called  a  keeper.  The  power  of  a 
magnet  is  measured  by  the  weight  its  poles  are  able  to 
carry. 

There  are  many  different  ways  in  which  magnetism 
can  be  imparted  to  needles  or  steel  bars,  as,  for  example, 

What  takes  place  when  a  large  key  suspending  several  small  ones  is  re- 
moved from  the  magnetic  atmosphere?  What  is  induction?  What  is 
the  nature  of  the  induced  polarity?  How  does  the  force  of  magnetic 
action  vary  ?  Can  one  species  of  magnetism  be  separated  from  the  other  ? 
What  is  meant  by  a  magnet  being  armed  ?  What  is  a  keeper  ? 


282  COMMUNICATION    OF    MAGNETISM. 

by  contact,  by  induction,  by  certain  movements.  By  the 
aid  of  voltaic  currents,  hereafter  to  be  described,  the 
most  intense  magnetic  power  can  be  communicated. 

The  process  of  magnetization  by  the  single  toucli  is  that 
in  which  we  place  one  pole  of  a  magnet  in  the  middle  of 
the  steel  bar,  and,  drawing  it  toward  the  end,  then  lifting 
it  up  in  the  air  return  it  to  its  former  position,  and  repeat 
the  movement  several  times.  The  magnet  is  now  to  be 
reversed,  and  in  that  position  moved  to  the  opposite  end 
of  the  bar,  lifted  up  in  the  air,  replaced,  and  the  move- 
ment many  times  repeated.  The  bar  thus  becomes  a 
magnet,  each  end  having  a  pole  opposite  to  that  by  which 
it  was  touched.  Or  we  may  place  two  magnets  with 
their  opposite  poles  in  the  middle  of  the  bar,  and  then, 
drawing  them  apart  in  opposite  directions,  the  same 
result  arises.  A  still  more  powerful  magnetism  may  be 
given  if  the  bar  to  be  magnetized  is  laid  on  the  poles  of 
two  magnets,  so  that  the  contrary  pole  of  the  magnets 
and  bar  coincide. 

In  the  double  touch  two  bar-magnets  are  so  tied  to- 
gether that  their  opposite  poles  may  be  maintained  a 
short  distance  from  one  another.  This  combination  is 
then  placed  on  the  middle  of  the  bar  to  be  magnetized, 
and  drawn  toward  its  end  ;  but  as  soon  as  it  reaches  that 
without  passing  over  it,  it  is  returned  to  the  other  end 
with  a  reverse  motion,  and  then  back  again  ;  and  after 
this  has  been  done  several  times  the  process  is  ended  by 
drawing  the  combination  off  sideways,  when  it  is  at  the 
middle  of  the  bar. 


Describe  some  of  the  methods  by  which  magnetism  may  be  imparted. 
Describe  the  process  by  single  touch.    What  is  that  by  double  touch? 


MARINER  S    COMPASS. 


283 


LECTURE  LVII. 

TERRESTRIAL  MAGNETISM. — Mariner's  Compass. — Mag- 
netic Variation. — Lines  of  Equal  Declination. — Dipping- 
Ncedle. — Lines  of  Equal  Dip. — Magnetic  Terrestrial 
Poles. —  The  Earth's  Inductive  Action. — Lines  of  Equal 
Intensity. — Magnetameters. — Secular  and  Diurnal  Va- 
riation.— Irregular  Disturbances. —  Terrestrial  Magnet- 
ism due  to  the  Heat  of  the  Sun. 

WHEN  a  magnetic  needle  is  suspended  on  a  pivot  so 
as  to  have  freedom  of  motion  horizontally,  it  sets  itself 
nearly  in  a  direction  north  and  south,  and  constitutes  a 
compass. 

In  the  mariner's  compass  a  light  card  is  attached  to 
the  needle;  on  it  there  is  drawn  a  circle  divided  into  thirty- 
two  parts.  This  accompanies  the  motion  of  the  needle, 
and  as  the  instrument  is  constantly  liable  to  be  thrown 
into  a  variety  of  positions  by  the  motions  of  the  ship,  it  is 
supported  in  gynAals,  as  shown  in  Fig.  305.  This  con- 

.  305. 


trivance  consists  of  two  pair  of  pivots,  E  E,  P  P,  set 
upon  rings  at  right  angles  to  one  another,  and  the  bottom 

What  is  a  compass  ?    How  is  the  mariner's  compass  arranged  ?    What 
are  gymbals? 


284 


THE    DIPPING-NEEDLE. 


of  the  compass-box  being  heavy  it  is  immaterial  what 
position  is  given  to  it ;  it  always  sets  itself  with  the  card 
in  a  horizontal  plane.  Occasionally  the  box  is  accom- 
modated with  sights,  Gr  H. 

Accurate  observations  have  shown  that  the  magnetic 
needle  does  not,  however,  point  rigorously  north  and  south, 
except  in  a  few  restricted  positions,  on  the  earth's  surface. 
But  it  exhibits  in  most  places  a  declination  or  variation 
to  the  east  or  west  of  the  true  point.  If  the  places  in 
which  there  is  no  declination  be  connected  together,  the 
line  running  through  them  is  called  a  line  of  no  declina- 
tion, and  of  these  there  are  two,  one  the  American  and 
the  other  the  Asiatic.  These  have  a  general  direction 
from  the  north  to  the  south. 

By  lines  of  equal  declination  we  mean  those  lines 
which  pass  through  places  where  the  amount  of  declina- 
tion is  equal.  They  are  irregular  in  their  form,  but  have 
a  relation  to  the  magnetic  poles.  The  position  of  these, 
as  well  as  of  the  former  lines,  is  not  stable  :  it  varies  in 
the  course  of  time. 

When  a  needle  is  arranged  on  a  horizontal  axis,  so  as 

Fig.  300. 


Does  the  compass  point  accurately  north  and  south  ?  What  is  a  line  of 
no  declination  ?  How  many  are  there  ?  What  is  their  direction  ?  What 
are  lines  of  equal  declination  ?  Are  these  regular  curves  ? 


MAGNETISM  OF  THE  EARTH.          285 

to  move  in  a  vertical  plane,  it  constitutes  a  dipping-needle, 
of  which  a  representation  is  given  in  Fig.  306.  The 
points  of  the  needle,  N  S,  traverse  over  a  circle  divided 
into  degrees,  and  the  angle  which  such  a  needle  makes 
with  a  horizontal  line  is  the  angle  of  the  dip.  In  the 
northern  hemisphere  the  north  pole  dips ;  near  the  equa- 
tor the  needle  has  no  dip  ;  and  in  the  southern  hemi- 
sphere the  south  pole  dips. 

The  dip  of  the  needle  was  first  discovered  by  Norman, 
who  noticed  that,  after  a  mariner's  compass-needle  was 
magnetized  it  lost  its  horizontality,  and  required  a  little 
wax  or  some  small  weight  on  the  opposite  side  to  restore 
it  to  its  true  position. 

The  dip  of  the  needle  diifers  in  different  places.  Those 
points  of  the  earth  where  there  is  no  dip  being  connected 
together  by  a  line,  give  what  is  termed  the  magnetic 
equator.  It  is  a  very  irregular  curve  which  cuts  the 
geographical  equator  in  two  places,  so  that  in  the  western 
hemisphere  it  is  south  of  the  equator,  and  in  the  eastern 
north.  Lines  which  connect  places  where  the  dip  is 
equal  are  called  lines  of  equal  dip;  they  observe  a. gen- 
eral parallelism  to  the  magnetic  equator. 

All  the  magnetic  phenomena  exhibited  by  the  earth  in 
their  general  features  answer  to  what  ought  to  take  place 
were  the  earth  itself  a  great  magnetic  mass,  with  its  poles 
near,  but  not  coincident  with  the  geographical  poles.  On 
this  principle  the  polarity  and  the  dip  of  the  needle  are 
both  readily  explained.  Of  course  the  north  pole  of  the 
earth  possesses  analogous  properties  to  the  south  pole  of 
the  suspended  needle,  and  vice  versa.  Formerly  it  was 
believed  that  there  existed  two  terrestrial  poles  in  each 
hemisphere ;  but  there  is  reason  now  to  suppose  that 
there  is  but  one.  That  in  the  northern  hemisphere  was 
reached  by  Sir  James  Ross  in  1833. 

This  general  similitude  of  the  earth's  action  to  that  of 
a  magnet  is  still  further  jporne  out  by  the  inductive  influ- 
ence of  the  earth.  This  may  be  shown  in  a  very  striking 
manner,  by  taking  a  bar  of  soft  iron  and  bringing  it  near 

What  is  a  dipping-needle  ?  How  does  it  act  in  the  north  and  in  the 
south  hemispheres?  How  was  the  dip  first  discovered?  What  is  the 
magnetic  equator?  What  is  its  course  ?  What  are  lines  of  equal  dip? 
What  do  the  phenomena  of  terrestrial  magnetism  answer  to?  How 
many  magnetic  poles  are  there  ?  Has  the  magnetic  pole  ever  been  reached  ? 


286  MAGNETOMETERS. 

a  suspended  needle.  So  long  as  the  bar  is  in  a  horizon- 
tal position,  and  at  right  angles  to  the  middle  of  the  nee- 
dle, the  latter  is  unaffected ;  but,  on  turning  the  bar,  so 
that  its  length  may  coincide  with  the  line  of  dip,  its  lower 
pole  will  repel  the  north  pole  of  the  needle,  showing  that 
it  has  north  polarity ;  but  it  will  attract  the  south  pole. 
And  this  condition  remains  so  long  as  the  bar  remains  in 
its  position ;  but,  on  turning  it  over,  and  reversing  its  po- 
sition, its  magnetism  is  instantly  reversed,  showing  that 
the  whole  action  is  due  to  the  power  of  the  earth. 

Like  the  declination  and  the  dip,  the  absolute  intensity 
of  the  earth's  magnetism  varies  very  much  in  different 
places ;  at  the  magnetic  equator  being  most  feeble,  and 
gradually  increasing  as  we  go  the  poles.  Lines  connect- 
ing places  where  the  intensities  are  equal  are  lines  of  equal 
intensity.  This  absolute  intensity  is  estimated  by  the  num- 
ber of  oscillations  which  a  magnet  makes  in  a  given  time, 
being  thus  directly  as  the  number  of  oscillations  made  in 
one  minute.  The  declination-needle  gives  us,  by  its  os- 
cillations, a  measure  of  that  portion  of  terrestrial  magnet- 
ism which  acts  horizontally,  the  dipping-needle  that  which 
acts  vertically ;  but  it  may  be  shown  that  the  effect  of 
either  of  these  is  proportional  to  the  absolute  intensity. 
To  measure  these  effects,  instead  of  small  and  light  nee- 
dles being  used,  bars  of  several  pounds  weight  are  em- 
ployed. They  are  called  magnetometers. 

The  declination,  the  dip,  and  the  intensity  all  undergo 
variations  at  the  same  place  ;  some  of  which  are  regular 
and  others  irregular — some  occurring  through  long  pe- 
riods of  time,  and  others  at  short  intervals.  In  the  year 
1657,  the  declination  needle  pointed  due  north  in  Lon- 
don ;  it  then  commenced  moving  westward,  and  contin- 
ued to  do  so  till  the  close  of  last  century.  Its  variation 
is  now  decreasing.  The  daily  variation  consists  of  an  os- 
cillation eastward  or  westward  of  the  mean  position,  the 
amount  of  which  varies  with  the  times  of  the  day,  and  is 
different  in  different  places.  Generally  the  greatest  dec- 
lination eastward  is  between  six  and  nine  in  the  morning, 

How  may  the  earth's  inductive  action  be  established  by  experiment  ?  Is 
the  absolute  intensity  variable  ?  How  is  it  estimated  ?  What  do  the  decli- 
nation and  dipping-needles  respectively  indicate  ?  What  are  magnetome- 
ters? Are  the  declination,  dip,  and  intensity  constant  in  amount  ?  What 
variations  have  been  observed  in  the  needle  at  London  ? 


MAGNETIC    DISTURBANCES.  287 

and  westward  about  one  in  the  afternoon,  returning  to- 
ward the  east  until  eight  P.  M.  It  is  never  more  than  a  few 
minutes;  and  the  needle  is  stationary  at  night.  Changes 
in  the  weather  and  the  occurrence  of  storms  and  clouds 
have  also  an  influence  on  the  needle.  The  dipping-nee- 
dle exhibits  similar  phenomena;  and,  as  respects  the  in- 
tensity, it  is  greater  in  the  evening  than  the  morning,  and 
is  less  in  summer  than  in  winter. 

Besides  these,  there  are  regular  disturbances  of  the 
earth's  magnetism — such,  for  instance,  as  those  arising 
from  the  aurora  borealis,  which  will  sometimes  deflect 
the  needle  several  degrees.  Over  very  extensive  areas 
simultaneous  disturbances  have  been  noticed,  it  having 
been  established  that  the  minute  and  irregular  variations 
take  effect  at  the  Same  instant  in  places  at  great  distances 
apart. 

There  can  be  no  doubt  that  the  magnetism  of  the  earth 
is  very  intimately  connected  with  the  calorific  action  of 
the  sun.  Thus,  the  lines  of  equal  dip  closely  correspond 
to  the  lines  of  equal  heat — the  northern  magnetic  pole 
nearly  coincides  with  the  point  of  minimum  heat  on  the 
earth's  surface.  The  diurnal  variations,  in  some  measure, 
follow  the  temperature,  as  the  sun  shines  on  different  parts 
in  succession  ;  and  the  same  connection  with  inequality 
of  heating  is  traced  in  the  annual  variation.  When  we 
come  to  describe  thermo-electric  currents — currents  ex- 
cited by  heat — and  trace  the  effect  of  these  currents  on 
the  suspended  needle,  we  shall  have  a  clearer  idea  of  the 
nature  of  these  obscure  phenomena. 

What  are  the  diurnal  variations  ?  At  what  periods  do  they  occur?  What 
influence  does  the  aurora  borealis  exert  ?  What  reasons  have  we  for  sup- 
posing that  the  magnetism  of  the  earth  is  connected  with  the  calorific  ac- 
tion of  the  sun  ? 


288  ELECTRICITY. 


ELECTRICITY. 


LECTURE  LVIII. 

ELECTRICITY. — First  Discoveries  in  Electricity. — Leading 
Phenomena. — Conductors,  Non-conductors,  and  Insula- 
tion.—  Two  Kinds  of  Electricity. —  Vitreous  and  Posi- 
tive, Resinous  and  Negative. — Law  of  Electrical  Attrac- 
tion and  Repulsion. — Plate  Machine. —  Cylinder  Ma- 
chine.—  Miscellaneous  Electrical  Experiments. —  The 
Two  Theories  of  Electricity. 

MORE  than  two  thousand  years  ago  it  was  discovered 
that  when  amber  is  rubbed  it  acquires  the  property  of 
attracting  light  bodies.  This  incident  has  served  to  give 
a  name  to  the  agent  whose  operations  we  have  now  to 
explain,  which  has  been  called  electricity,  from  TjkeiCTpov, 
a  Greek  word,  signifying  amber. 

A  great  number  of  other  bodies  possess  the  same  qual- 
ity ;  among  these  may  be  mentioned  glass,  sealing-wax, 
resin,  silk.  They,  too,  when  rubbed,  can  attract  light 
substances,  and,  when  the  excitement  is  vigorous,  emit 
sparks  like  those  which  are  seen  when  the  back  of  a  cat 
is  rubbed  on  a  frosty  night.  It  is  not  improbable  that  it 
was  from  observing  this  singular  phenomenon  that  the 
Egyptians  were  induced  to  regard  that  animal  as  sacred. 

If  a  piece  of  brown  paper  be  thoroughly  dried  at  the 
fire  until  it  begins  to  smoke,  and  then  rubbed  between 
woollen  surfaces,  it  will  emit  sparks  on  the  approach  of 
the  finger,  attract  pieces  of  light  paper,  and  then  repel 
them.  This  latter  phenomenon  is  not,  however,  peculiar 
to  it,  but  is  noticed  in  the  case  of  all  highly-excited  bodies. 

When  were  electrical  phenomena  first  observed?  What  circum- 
stance has  given  to  this  agent  a  name?  Mention  some  other  electrics. 
What  experiments  may  be  made  with  dry  brown  paper? 


CONDUCTORS    AND    NON-CONDUCTORS.  289 

• 

Electrified  bodies,  therefore,  exhibit  repulsions  as  well  as 
attractions. 

Let  there  be  taken  a  glass  tube,  a  b,  Fig.  307,  an  inch 
in  diameter  and  a  foot  or  Fig.yn. 

more  long,  closed  at  the  end,    a  b 

b,  by  means  of  a  cork,  into  ~J_  ~~tsj  QC 

which  there  is  inserted  a  wire 

with  a  round  ball,  c.  If  the  tube  be  excited  by  rubbing 
with  a  piece  of  dry  silk  it  may  be  shown  that  not  only 
does  the  space  rubbed  possess  the  powers  of  attraction 
and  repulsion,  but  also  the  cork  and  the  ball.  Nor  does 
it  matter  how  long  the  wire  may  be,  the  electric  power  is 
transmitted  through  the  whole  of  the  metal.  A  metal, 
therefore,  can  conduct  electricity. 

But  if,  instead  of  a  piece  of  metal,  we  terminate  the 
glass  tube  with  a  rod  of  glass  or  sealing-wax,  or  hang  a 
ball  to  it  by  a  thread  of  silk,  in  all  these  cases  the  electric 
power  cannot  pass.  Such  substances  are,  therefore,  non- 
conductors of  electricity. 

When  electricity  is  communicated  to  a  body  which  is 
supported  on  any  of  these  non-conducting  substances,  its 
escape  is  cut  off,  and  the  body  is  said  to  be  insulated. 

From  a  silk  thread  which  is  fastened  to  a  stand,  c,  Fig. 
308,  let  there  be  suspended  a  feather,  b;  let  Fig.  MS. 
this  be  electrified  by  a  glass  rod^a,  highly  ex- 
cited. The  feather  is  at  first  attracted  and 
then  repelled.  On  the  approach  of  the  exci- 
ted glass  it  instantly  recedes,  attempting,  as 
it  were,  to  get  out  of  its  way.  Now,  instead 
of  the  glass  rod,  a,  let  us  present  a  stick  of 
excited  sealing-wax,  or  a  roll  of  sulphur — the 
feather  is  instantly  attracted,  and,  therefore,  this  remark- 
able experiment  proves  that  the  electric  virtue  which  ema- 
nates from  excited  bodies  is  not  always  the  same,  and  that 
a  body  which  is  repelled  by  excited  glass  is  attracted  by 
excited  wax. 

Extensive  inquiry  has  shown,  that  in  reality  there  are 
two  species  of  electricity,  to  which  names  have  therefore 

What  results  may  be  shown  by  the  instrument,  Fig.  307  ?  How  may  it 
be  shown  that  metals  conduct  electricity  ?  How  may  it  be  proved  that 
other  bodies  are  non-conductors  ?  What  is  meant  by  insulation  ?  Prove 
that  there  are  two  different  sorts  of  electricity  ?  What  names  have  been 
given  to  them  ? 


290 


TWO    KINDS    OF    ELECTRICITY. 


been  given.  To  one — because  it  arises  from  the  friction 
of  glass — vitreous  electricity ;  and  to  the  other,  which 
arises  under  similar  circumstances  from  wax,  resinous 
electricity. 

The  relations  of  these  electrical  forces  to  one  another, 
as  respects  attraction  and  repulsion,  constitute  the  funda- 
mental law  of  this  department  of  science.  That  general 
law,  briefly  expressed,  is — "  Like  electricities  repel  and 
unlike  ones  attract."  That  is  to  say,  two  bodies  which 
are  both  vitreously  or  both  resinously  electrified,  will  re- 
pel each  other;  but  if  one  is  vitreous  and  the  other  res- 
inous, attraction  takes  place.  To  the  two  different  species 
of  electricity  synonymous  designations  are  sometimes  ap- 
plied. The  vitreous  is  called  positive,  and  the  resinous 
negative  electricity. 

For  the  sake  of  observing  electrical  phenomena  more 
Fig.  309.  readily,  instruments  have  been  in- 

vented, called  electrical  machines. 
They  are  of  two  kinds  :  the  plate 
machine  and  the  cylinder  ;  they 
derive  their  names  from  the  shape 
of  the  glass  employed  to  yield  the 
electricity.  The  plate  machine, 
Fig.  309,  consists  of  a  circular 
plate  of  glass,  a  a,  which  can  be 
turned  upon  an  axis,  b,  by  means 
of  a  winch,  c;  at  d  is  a  pair 
of  rubbers,  which  compress  tho 
glass  between  them,  and  a  piece 
of  oiled  silk  extends  over  the  glass  plate,  as  shown  at  e  ; 

in  the  same  manner,  on 
the  opposite  side  of  the 
plate,  there  is  another  pair 
of  rubbers,  d,  and  an  oiled 
silk,  e;  f  is  the  prime  con- 
ductor, which  gathers  the 
electricity  as  the  plate  re- 
volves. It  must  be  support- 
ed on  an  insulated  stem. 
The  cylinder  machine  is 

What  is  the  general  law  of  electrical  attraction  and  repulsion  ?  What 
names  are  given  to  the  two  sorts  of  electricity?  Describe  the  plate  ma- 
chine. Describe  the  cylinder  machine. 


c    Fig.  310. 


ELECTRICAL    MACHINES.  291 

represented  at  Fig.  310.  It  consists  of  a  glass  cylinder, 
a  «,  so  arranged  that  it  can  be  turned  on  its  axis  by  the 
multiplying-wheel,  b  b.  The  rubber  bears  against  the 
glass  on  the  opposite  side  to  that  seen  in  the  figure,  and 
the  oiled  silk  is  shown  at  c;  d  is  the  prime  conductor, 
usually  a  cylinder  with  rounded  ends,  made  of  thin  brass, 
and  e  its  insulating  support. 

Of  these  machines  the  plate  is  commonly  the  most  pow- 
erful- It  is  more  liable  to  be  broken  than  the  cylinder, 
from  the  disadvantageous  way  in  which  the  power  to 
turn  it  round  is  applied. 

To  bring  an  electrical  machine  into  activity,  it  must  be 
thoroughly  dried  ;  but  a  plate  machine  should'never  be  set 
before  the  fire  to  warm,  or  it  will  almost  certainly  crack. 
The  rubbers  are  to  be  spread  over  with  a  little  Mosaic 
gold,  or  amalgam  of  zinc,  and  the  stem  of  the  conductor 
made  dry.  If  the  rubbers  of  the  machine  are  not  in  con- 
nection with  the  ground,  there  must  be  a  chain  hung  from 
them  to  reach  the  table.  Then,  when  the  instrument  is 
in  activity,  on  presenting  the  finger  to  the  prime  conduct- 
or a  succession  of  sparks  is  emitted,  attended  with  a  crack- 
ling sound. 

A  great  many  beautiful  experiments  may  be  made  by 
the  aid  of  this  machine.  They  are  for  the  most  part  il- 
lustrations of  the  luminous  effects  of  the  spark,  attractions 
and  repulsions,  and  certain  physiological  results,  as  the 
electrical  shock. 

If  there  be  pasted  on  a  slip  of  glass  a  continuous  line 

of  tin  foil,  as  shown  in  Fig.  311,      F»g.  sn. . 

and  then  letters  be  cut  out  of  it  ~~ 
with  a  sharp  knife,  on  present- 
ing  the  ball,  G-,  which  commu- 
nicates with  the  tin  foil  to  the  prime  conductor,  and  touch- 
ing the  point,  a,  with  the  finger,  the  electric  fluid  will  run 
along  the  metallic  line,  leaping  over  each  interspace,  in 
the  form  of  a  short  but  brilliant  spark,  and  marking  out 
the  letters  in  a  beautiful  manner. 

A  tube  several  feet  long,  with  a  ball  at  one  end  and  a 
stop- cock  at  the  other,  is  to  be  exhausted  of  air.  On  pre- 
senting the  ball  to  the  prime  conductor,  the  electricity 

Which  of  the  two  is  more  powerful  ?  How  are  they  brought  into  ac- 
tion ?  How  may  words  be  written  by  the  electric  spark  ?  What  phe« 
nomena  are  exhibited  by  an  exhausted  tube  ? 


292  ELECTRICAL    EXPERIMENTS. 

passes  down  the  whole  length  of  the  exhausted  tube  as  a 
pale  milky  flame,  but  giving  now  and  then  brilliant  flashes, 
especially  when  the  tube  is  touched.  The  phenomenon 
has  some  resemblance  to  that  of  the  Northern  lights. 
Fig.  312.  Between  two  metallic  plates,  a  b,  Fig.  312,  of 
which  a  is  hung  by  a  chain  to  the  prime  con- 
ductor, and  b  supported  on  a  conducting  stand, 
let  some  figures,  made  of  paper,  pith,  or  other 
light  body,  be  placed.  The  plates  maybe  three 
or  four  inches  apart.  On  throwing  the  machine 
into  activity  the  figures  are  alternately  attracted 
and  repelled,  and  move  about  with  a  dancing 
motion.. 

From  a  brass  rod,  a  c  b,  Fig.  313,  which  may  be  hung 
by  an  arch,  g,  to  the  prime  conductor, 
three  bells  are  suspended — two  from  a 
and  b  by  chains,  and  the  middle  one, 
c,  by  a  silk  thread — between  the  bells 
two  little  metallic  clappers,  d  e,  are  hung 
by  silk,  and  from  the  inside  of  the  mid- 
dle bell  a  chain,  f,  hangs  down  upon  the 
table.  On  setting  the  electrical  machine  in  activity,  the 
clappers  commence  moving  and  ring  the  bells.  This  in- 
strument has  been  employed  in  connection  with  insulated 
lightning-rods,  to  give  warning  of  the  approach  of  a  thun- 
der-cloud. 

To  account  for  the  various  phenomena  of  electricity, 
two  theories  have  been  invented.  They  pass  under  the 
names  of  Franklin's  theory,  or  the  theory  of  one  fluid, 
and  Dufay's  theory,  or  the  theoiy  of  two  fluids. 

Franklin's  theory  is,  that  there  exists  throughout  all 
space  an  ethereal  and  elastic  fluid,  which  is  characterized 
by  being  self-repulsive — that  is,  each  of  its  particles  repels 
the  others ;  but  it  is  attractive  of  the  particles  of  all  other 
matter.  To  this  the  name  of  electric  fluid  has  been  given. 
Different  bodies  are  disposed  to  assume  particular  or  spe- 
cific quantities  of  this  fluid,  and  when  they  have  the  amount 
that  naturally  belongs  to  them,  they  are  said  to  be  in  a 
natural  state  or  condition  of  equilibrium.  But  if  more  than 

Describe  the  experiment  of  the  dancing  figures.  Describe  the  electrical 
bells.  For  what  purpose  have  they  been  used  ?  How  many  theories  of 
electricity  are  there  ?  What  is  Franklin's  theory?  In  what  consists  the 
natural,  the  positive,  and  negative  state  of  bodies  according  to  it  ? 


ELECTRICAL   THEORIES.  293 

the  natural  quantity  is  communicated  to  them,  they  be- 
come positively  electrified;  and  if  they  have  less  than  their 
natural  quantity,  they  are  negatively  electrified. 

The  theory  of  two  fluids  is,  that  there  exists  an  ethere- 
al medium,  the  immediate  properties  of  which  are  not 
known.  It  is  composed  of  two  species  of  electricity — 
the  positive  and  the  negative — each  of  these  being  self- 
repellent,*but  attractive  of  the  other  kind.  Bodies  are  in 
a  neutral  or  natural  state  or  condition  of  equilibrium, 
when  they  contain  equal  quantities  of  the  two  electrici- 
ties ;  and  they  are  positively  electrified  when  the  positive 
is  in  excess,  and  negative  when  the  negative  is  in  excess. 

Of  these  two  theories,  it  appears  that  the  latter  will  ac- 
count for  the  greater  number  of  phenomena. 


LECTURE  LIX. 

INDUCTION,  DISTRIBUTION,  AND  MEASUREMENT  OP  ELEC- 
TRICITY.—  Electrical  Induction. — The  Ley  den  Jar. — 
Its  Effects. — Dr.  Franklin's  Discovery. —  The  Light- 
ning-Rod.— Distribution  of  Electricity. — Pointed  Bodies. 
—  Velocity  of  Electricity. — Modes  of  Developing  Elec- 
tricity.— Zamboni's  Piles. — Perpetual  Motion. — Elec- 
troscopes.— Electrometers. 

BY  electrical  INDUCTION  is  meant  that  a  body  in  an 
electrified  state  is  able  to  induce  an  analogous  condition 
in  others  in  its  neighborhood  without  being  in  immediate 
contact  with  them. 

This  effect  arises  from  the  general  law  of  attraction  and 
repulsion ;  for  the  natural  condition  of  bodies  is  such  that 
they  contain  equal  quantities  of  positive  and  negative  elec- 
tricity ;  and,  when  this  is  the  case,  they  are  said  to  be  in 
the  neutral  state,  or  in  a  condition  of  equilibrium. 

When,  therefore,  an  electrified  body  is  brought  into 
the  neighborhood  of  a  neutral  one,  both  being  insulated, 
disturbance  immediately  ensues.  The  electrified  body 
separates  the  two  electricities  of  the  neutral  body  from 

What  is  Dufay's  theory  ?  How  does  it  account  for  the  corresponding 
states  of  bodies  "?  What  is  meant  by  electrical  induction  ?  What  is  the 
natural  condition  of  bodies  ?  How  does  an  electrified  body  disturb  a  neu- 
tral one  ? 


294  THE    LBYDEN    JAR. 

each  other,  repelling  that  of  the  same  kind,  and  attract- 
ing that  of  the  opposite.  Thus,  if  a  body  electrified  pos- 
itively be  brought  near  one  that  is  neutral,  the  positive 
electricity  of  this  last  is  repelled  to  the  remoter  part,  but 
the  negative  is  attracted  to  that  part  which  is  nearest  the 
disturbing  body. 

The    Leyden  jar,  Fig.  314,  is  a  glass  jar,  coated  on  the 
Fig.  314.       inside  arid  outside  with  tin  foil  to  within  an 
inch  OP  two  of  the  edge.     Through  the  cork 
which  closes  the  mouth  a  brass  wire  reaches 
down,  so  as  to  be  in  contact  with  the  inside 
coating,  and  terminates  at  its  upper  end  in 
a  ball.     On  connecting  the  outside   coating 
with   the  ground,  and   presenting   the   ball 
to  the  prime  conductor,  a  large  amount  of 
electricity  is  received  by  the  machine  ;  and 
-*•  if  it  be  touched  on  the  outside  by  one  hand, 
and  communication  be  made  with  the  ball   by  the  other, 
a  very  bright  spark  passes,  and  the   electric   shock  is 
felt.    ' 

The  mechanical  effects  of  lightning  may  be  represented 
in  a  small  way  by  this  instrument.  On  passing  a  strong 
shock  through  a  piece  of  wood  it  may  be  torn  open,  and 
other  resisting  media  may  be  burst  to  pieces.  The  shock 
passed  through  a  card  perforates  it. 

Dr.  Franklin  discovered  the  identity  of  lightning  and 
electricity.  He  established  this  important  fact  by  raising 
a  kite  in  the  air  during  a  thunder-storm.  The  string  of 
the  kite,  which  was  of  hemp,  terminated  in  a  silken  cord, 
and  at  the  point  where  the  two  were  attached  a  key  was 
hung.  The  electricity,  therefore,  descended  down  the 
hempen  string,  but  was  insulated  by  the  silk,  and  on  pre- 
senting a  finger  to  the  key,  sparks  in  rapid  succession 
were  drawn.  It  is  on  this  fact  that  the  lightning-rod 
for  the  protection  of  buildings  depends.  A  metallic  rod  pro- 
jects above  the  top  of  the  building,  and  descends  down 
to  a  certain  depth  in  the  ground,  offering,  therefore,  a  free 
passage  for  the  electric  fluid  into  the  earth. 

When    electricity  is    communicated    to    a  conducting 

Describe  the  Leyden  jar.  How  is  it  charged  and  discharged?  What  ef- 
fects may  be  produced  by  it  ?  How  and  by  whom  was  the  identity  of 
lightning  and  electricity  proved?  What  is  the  principle  of  the  lightning- 


DISTRIBUTION    OF    ELECTRICITY.  295 

body  it  resides  merely  upon  the  surface,  and  does  not 
penetrate  to  any  depth  within^  In  the  case  of  spherical 
bodies,  this  superficial  distribution  is  equal  all  over ;  but 
when  the  body  to  which  the  electricity  is  communicated 
is  longer  in  one  direction  than  the  other,  the  electricity 
is  chiefly  found  at  its  longer  extremities,  the  quantity  at 
any  point  being  proportional  to  its  distance  from  the 
center. 

These  principles  may  be  very  well  illustrated  by  taking 
a  long  strip  of  tin  foil,  so  arranged  as  to  be  rolled  and  un- 
rolled upon  a  glass  axis,  and  connected  with  a  pair  of 
cork  balls,  the  divergence  of  which  shows  its  electrical 
condition.  If,  now,  to  this,  when  coiled  up,  a  sufficient 
amount  of  electricity  is  communicated  to  make  the  balls 
diverge,  on  pulling  out  the  tin  foil,  so  as  to  have  a  larger 
surface,  they  will  collapse ;  but  on  winding  the  foil  up 
again  they  will  again  diverge,  showing  that  the  distribu- 
tion of  electricity  is  wholly  superficial,  and  that  when  a 
given  quantity  is  spread  over  a  large  surface  it  necessa- 
rily becomes  weaker  in  effect. 

In  the  case  of  pointed  bodies,  the  length  of  which  is 
very  great  compared  with  their  other  dimensions,  the 
chief  accumulation  of  electricity  takes  place  upon  the 
point.  When  a  needle  is  fastened  upon  a  prime  con- 
ductor, this  accumulation  becomes  so  great  that  the  fluid 
escapes  into  the  air,  and  may  be  seen  in  the  dark  in  the 
form  of  a  luminous  brush.  Or  if,  on  the  other  hand,  a 
needle  be  presented  to  a  prime  conductor  it  withdraws 
its  electricity  from  it,  and  the  point  becomes  gilded  with  a 
little  star. 

The  electric  fluid  moves  with  prodigious  rapidity.  It 
has  a  Telocity  greatly  exceeding  that  of  light.  In  a  cop- 
per wire  its  velocity  is  288,000  miles  in  one  second. 

There  are  many  different  ways  in  which  electricity 
may  be  developed.  In  the  processes  we  have  hitherto 
described  it  originates  in  friction.  And,  as  one  kind  of 
electricity  can  never  make  its  appearance  alone,  but  is 
always  accompanied  with  an  equal  quantity  of  the  other, 

Does  electricity  reside  on  the  surface  or  in  the  interior  of  bodies  ?  How 
is  its  distribution  dependent  on  their  figure?  How  may  it  be  proved  that 
electricity  is  distributed  superficially?  What  is  the  effect  of  pointed 
bodies?  How  may  a  brush  and  a  star  of  light  be  exhibited  ?  What  is  the 
velocity  of  the  electric  fluid  ?  By  what  processes  may  electricity  be  devel- 
oped ?  Can  one  kind  of  electricity  be  obtained  without  the  other  ? 


296 

•we  uniformly  find  that  the  rubber  and  the  surface  rubbed 
are  always  in  opposite  states — if  the  one  is  positive  the 
other  is  negative.  It  is  on  this  principle  that  many  ma- 
chines are  furnished  with  means  of  collecting  the  fluid 
from  the  prime  conductor  or  the  rubber,  and,  therefore, 
of  obtaining  the  positive  or  negative  electricity  at  pleas- 
ure. 

Electricity  may  also  be  developed  by  heat.  The  tour- 
maline, a  crystalized  gem,  when  warmed,  becomes  posi- 
tive at  one  end  and  negative  at  the  other.  Changes  of 
form  and  chemical  changes  of  all  kinds  give  rise  to  elec- 
tric development. 

Zamboni's  electrical  piles  are  made  by  pasting  gold 
leaf  on  one  side  of  a  sheet  of  paper  and  thin  sheet  zinc 
on  the  other,  and  then  punching  out  of  it  a  number  of 
circular  pieces  half  an  inch  in  diameter.  If  several  thou- 
sands of  these  be  packed  together  in  a  glass  tube,  so  that 
their  similar  metallic  faces  shall  all  look  the  same  way, 
Fig.  315.  and  be  pressed  tightly  together  at  each 
end  by  metallic  plates,  it  will  be  found 
that  one  extremity  of  the  pile  is  positive 
and  the  other  negative  ;  and  that  the  ef- 
fect continues  for  a  great  length  of  time. 
Fig.  315  represents  a  pair  of  these  piles, 
arranged  so  as  to  produce  what  was,  at 
one  time,  regarded  as  a  perpetual  motion. 
Two  piles,  a  Z>,  are  placed  in  such  a  po- 
sition that  their  poles  are  reversed,  and 
between  them  a  ring  or  light  ball,  c,  vi- 
brates like  a  pendulum  on  an  axis,  d.  It 
is  alternately  attracted  to  the  one  and  then  to  the  other, 
and  will  continue  its  movements  for  years.  A  glass  shade 
is  placed  over  it  to  protect  it  from  external  disturbance. 

The  purposes  of  philosophy  require  means  for  the 
detection  and  measurement  of  electricity.  The  instru- 
ments for  these  uses  are  called  electroscopes  and  elec- 
trometers ;  they  are  of  different  kinds. 

A  pair  of  cork  balls,  a  a,  Fig.  316,  suspended  by  cot- 
ton threads  so  as  to  hang  parallel  to  one  another,  and  be 
in  metallic  communication  with  the  ball,  b,  furnish  a  sim- 

What  are  the  phenomena  of  the  tourmaline  ?  "What  are  Zamboni's 
electrical  piles?  How  may  these  be  made  to  furnish  an  apparent  perpet- 
ual motion? 


ELECTROMETERS. 


297 


pie  instrument  of  the  kind.  If  any  electricity  is  commu- 
nicated to  b,  the  balls  participate  in  it,  and  as 
bodies  electrified  alike  repel,  these  recede 
from  each  other.  The  amount  of  their  diverg- 
ence gives  a  rough  estimate  of  the  relative 
quantity  of  electricity.  All  delicate  electrome- 
ters should  be  protected  from  currents  in  the 
air  by  means  of  a  glass  cylinder  or  shade,  as  c  c.  ''  *' 

The  gold  leaf  electroscope  differs  from  the  foregoing 
only  in  the  circumstance  that,  instead  of  a  pair  of  threads 
and  cork  balls,  it  has  a  pair  of  gold  leaves,  the  good  con- 
ducting power  and  extreme  flexibility  of  which  adapt 
them  well  for  this  purpose. 

The  quadrant  electrometer,  Fig.  317,  is  formed 
of  an  upright  stem,  a  b,  on  which  is  fastened  a 
graduated  semicircle  of  ivory,  c,  from  the  center 
of  which  hangs  a  cork  ball,  d.  As  this  is  repelled 
by  the  stem  the  graduation  serves  to  show  the 
number  of  degrees.  But  no  quantity  of  electricity 
can  ever  drive  it  beyond  90° ;  and,  indeed,  its 
degrees  are  not  proportional  to  the  quantities  of 
electricity. 

The   best    electrometer    is   Coulomb's    torsion 


Fig.  317. 


IS 

trometer,  Fig.  318,  of  which  a  de- 
scription has  been  given  in  Lecture 
XXIII. 

The  best  electroscope  is  Bohnen- 
berger's.     It  consists  of  a  small  dry 
pile,  a  b,  Fig.  319,  supported  hori- 
zontally beneath  a  glass  shade,  and 
Fig.  319.         from  its  extremities, 
a    bt    curved    wires 
pass,  which  terminate 
in  parallel  plates,  p 
m.     One  of  these  is, 
therefore,   the   posi- 
tive,  and   the    other 
the  negative  pole  of 
the   pile.      Between 
them  there  hangs  a 


elec- 


Fig.  318. 


Describe  the  cork-ball  electroscope.  Describe  the  gold-leaf  electroscope. 
What  is  the  quadrant  electrometer?  Which  is  the  best  electrometer? 
Which  is  the  best  electroscope  T  Describe  it. 

N* 


298  THE  VOLTAIC  BATTERY. 

gold  leaf,  d  g,  which  is  in  metallic  communication  with  die 
plate,  o  n,  by  means  of  the  rod,  c.  If  the  leaf  hangs  equally 
between  the  two  plates,  it  is  equally  attracted  by  each,  and 
remains  motionless ;  but  on  communicating  the  slightest 
trace  of  electricity  to  the  plate,  o  n,  the  gold  leaf  instantly 
moves  toward  the  plate  which  has  the  opposite  polarity. 


LECTURE  LX 

THE  VOLTAIC  BATTERY. —  The  Voltaic  Pile. —  The  Trough. 
— Grove's  Battery.  —  Phenomena  of  the  Battery. — 
Sparks. — Incandescence.  —  Decomposition  of  Water. — 
Electromotive  Force. — Resistance  to  Conduction. — Power 
of  the  Battery. — Phenomena  of  a  Simple  Circle. 

THE  voltaic  pile  has  a  very  close  analogy  in  its  con- 
struction with  the  dry  piles  just  described.     It  consists  of 
a  series  of  zinc  and  copper  plates,  so  arranged  that  the 
Fig. wo.       same  order  is  continually  preserved,  and  be- 
tween them  pieces  of  cloth,  moistened  with 
acidulated  water — thus,  copper,  cloth,  zinc ; 
copper,  cloth,  zinc,   &c.     There   should   be 
from  thirty  to  fifty  such  pairs  to  form  a  pile 
of  sufficient  power. 

When  the  opposite  poles  or  ends  of  this  in- 
strument are  touched,  a  shock  is  at  once  felt.  It  is  not 
unlike  the  shock  of  a  Leyden  jar;  but  the  pile  differs  from 
the  electrical  machine  in  the  circumstance  that  it  can  at 
once  recharge  itself,  and  gives  a  shock  of  the  same  strength 
as  often  as  it  is  touched. 

As  the  voltaic  battery  is  now  employed  for  numerous 
purposes  in  science,  many  forms  more  convenient  than 
that  described,  have  been  introduced.      In   the  voltaic 
Fig.  321.  trough  the   zinc    and 

copper  plates  being 
soldered  together,  are 
let  into  grooves  in  a 
box,  as  shown  in  Fig. 
321,  the  cells  between 
each  pair  of  plates 

Describe  the  voltaic  pile.     Under  what  circumstances  does  it  give  a 
shock  1    What  is  the  form  given  to  this  instrument^  the  voltaic  trough  ? 


GROVE'S  BATTERY.  299 

serving  to  hold  the  mixture  of  water  and  sulphuric  acid. 
Such  an  instrument  is  easily  brought  into  activity,  and  its 
exciting  fluid  easily  removed. 

Of  late  other  more  powerful  forms  of  voltaic  battery 
have  been  invented ;  such,  for  instance,  as  Grove's  and 
Bunsen's.  Grove's  battery  consists  of  a  cylinder  of  zinc, 
Z,  Z,  Fig.  322,  the  surface  of  which  is  amalgamated  with 
quicksilver.  It  is  placed  in  a  glass  jar,  G  G.  Fig.  303. 
Within  this  there  is  a  cylinder  of  porous  earth- 
enware, p  p,  in  which  stands  a  sheet  of  pla-  z( 
tinum,  P  P.  In  Bunsen's  battery  P  is  a  cylin- 
der of  carbon,  into  which,  at  r,  a  polar  wire 
can  be  fastened.  The  glass  cup,  G  G,  is  filled  G 
with  dilute  sulphuric  acid  (a  mixture  of  one  of 
acid  to  six  of  water), the  porous  cylinder  is  fill- 
ed with  strong  nitric  acid,  and  the  amalgamated  zinc  is 
therefore  in  contact  with  dilute  sulphuric  acid,  and  the  pla- 
tinum or  carbon  with  nitric  acid.  By  means  of  the  bind- 
ing screws  polar  wires  maybe  fastened  to  the  plates,  and 
a  number  of  jars  may  be  connected  together  so  as  to  form 
a  compound  battery.  In  this  case,  the  wire  coming  from 
the  zinc  of  one  cup  is  to  be  connected  with  the  platinum 
or  carbon  of  the  next,  the  same  arrangement  being  con- 
tinued throughout. 

When  several  such  cups  are  connected  together,  and 
the  polar  wires  of  the  terminal  pairs  brought  in  contact, 
a  bright  spark,  or  rather  flame,  instantly  passes,  and  when 
these  connecting  wires  are  of  copper  the  color  of  the  light 
is  of  a  brilliant  green.  By  fastening  on  one  of  the  polar 
wires  conducting  substances  of  different  kinds,  they  burn 
or  deflagrate  with  different  phenomena,  each  metal  yield- 
ing a  colored  light.  If  a  fine  iron  or  steel  wire,  in  con- 
tact with  one  of  the  poles,  be  lowered  down  on  some 
quicksilver  into  which  the  other  is  immersed,  a  brilliant 
combustion  ensues — the  iron,  as  it  burns,  throwing  out  in- 
numerable sparks ;  and  on  pointing  the  polar  wires  with 
pieces  of  hard-burnt  charcoal,  on  approaching  them  to 
each  other  a  spark  passes,  and  the  points  may  now  be 
drawn  apart  several  inches,  if  the  battery  is  powerful,  the 

Describe  Grove's  battery.  In  this  battery  how  many  metals  and  liquids 
are  employed  ?  What  effect  ensues  when  the  connecting  wires  are  brought 
in  contact  ?  What  phenomena  do  the  different  metals  exhibit  during 
combustion  ?  What  ensues  ^vhen  charcoal-points  are  employed  ? 


300 


DECOMPOSITION    OF    WATER. 


Fig.  323. 

XTrt 


flame  still  continuing  to  play  between  them.  This  flame, 
which  is  arched  upward,  affords  the  most  brilliant  light 
that  can  be  obtained  by  any  artificial  process. 

If,  between  the  polar  wires  of  a  voltaic  battery,  a  piece 
of  platinum — a  metal  of  extreme  infusibility — intervenes, 
and  the  metal  withstands  fusion  and  is  not  too  thick,  it  be- 
comes incandescent,  and  continues  so  while  the  current 
passes. 

But  by  far  the  most  valuable  effects  to  which  these  in- 
struments give  rise  are  decompositions.  If  the  poles  of 
a  battery  are  terminated  with  pieces  of  platinum,  and 
these  are  dipped  in  some  water,  bubbles  of  gas  rapidly 
escape  from  each — they  arise  from  the  decomposition  of 
the  water. 

The  apparatus  Fig.  323,  enables  us 
to  perform  this  experiment  in  a  very 
satisfactory  manner.  It  consists  of  two 
tubes,  o  h,  which  have  lateral  open- 
ings,^? p,  through  which,  by  means  of 
tight  corks,  platinum  wires,  terminat- 
ed by  a  little  bunch  of  platinum,  may 
be  passed.  The  tubes,  o  h,  are  sus- 
pended vertically,  in  a  small  reser- 
voir of  water,  g,  by  an  upright,  V. 
They  are  also  graduated  into  parts 
of  equal  capacity.  By  means  of  the 
binding  screws  at  a  and  b  the  plati- 
num wires  may  be  connected  with  the  poles  of  an  active 
battery. 

If,  now,  the  two  tubes  are  filled  with  water  and  im- 
mersed in  the  trough,  and  the  communications  with  the 
battery  established,  gas  rapidly  rises  in  each,  and  collects 
in  its  upper  part.  In  that  tube  which  is  in  connection 
with  the  positive  pole  of  the  battery  oxygen  accumulates, 
in  the  other  hydrogen.  And  it  is  to  be  observed  that  the 
quantity  of  the  latter  is  equal  to  twice  the  quantity  of  the 
former  gas.  Water  contains  by  volume  twice  as  much 
hydrogen  as  it  does  oxygen. 

In  any  voltaic  combination,  the  exciting  cause  of  the 
electricity,  whatever  it  may  be,  goes  under  the  name  of 

Can  platinum  be  made  continuously  incandescent  ?  Describe  the  pro- 
cess for  the  decomposition  of  water.  What  are  the  relative  quantities  of 
oxygen  and  hydrogen  gases  produced  in  this  experiment  ? 


SIMPLE,  CIRCLE.  301 

the  electromotive  force,  and  the  resistances,  which  ob- 
struct the  motion  of  the  electricity,  are  termed  resist- 
ances to  conduction. 

The  electromotive  force  determines  the  amount  of  elec- 
tricity which  is  set  in  motion ;  and  in  a  voltaic  battery 
tne  resistances  which  arise  are  chiefly  due  to  the  imper- 
fect conducting  power  of  the  liquid  and  metalline  parts. 

The  resistance  of  the  metalline  parts  is  directly  as  their 
lengths  and  inversely  as  their  sections.  A  wire  two  feet 
long  resists  twice  as^much  as  a  wire  one  foot,  if  their  sec- 
tions are  equal ;  and  of  two  wires  that  are  of  an  equal 
length  that  which  has  a  double  thickness  or  section  will 
conduct  twice  as  well. 

The  resistance  of  the  liquid  parts  depends  on  the  dis- 
tance of  the  plates  from  one  another — it  is  inversely  as 
their  sections  of  those  parts. 

The  total  force  of  any  voltaic  battery  may  be  ascertain- 
ed by  dividing  the  sum  of  all  the  electromotive  forces  by 
the  sum  of  all  the  resistances 

The  origin  of  the  electrical  action  of  voltaic  combina- 
tions is,  in  all  probability,  due  to  chemical  changes 
going  on  in  them.  The  study  of  a  simple  voltaic  cir- 
cle throws  much  light  on  these  facts.  If  we  Fig.  324. 
take  a  plate  of  amalgamated  zinc,  z,  an  inch 
wide  and  six  long,  and  a  copper  plate,  c,  of 
equal  size,  and  dip  them  in  some  acidulated 
water  contained  in  a  glass  jar,^  they  form  a 
simple  voltaic  circle.  It  is  to  be  understood 
that  common  sheet  zinc  is  easily  covered  over 
with  quicksilver,  or  amalgamated,  by  washing  it 
with  sulphuric  acid  and  water  in  a  dish  in  which  some 
quicksilver  is  placed. 

Now,  so  long  as  the  two  plates  remain  side  by  side 
without  touching,  no  action  whatever  takes  place  ;  but  if 
we  establish  a  metallic  communication  between  them  by 
means  of  the  wire  d,  innumerable  bubbles  of  gas  escape 
from  the  copper,  c,  and  the  zinc  in  the  mean  time  slowly 
corrodes  away.  On  lifting  up  d  the  action  instantly  ceases, 

What  is  meant  by  the  term  electromotive  force  ?  What  by  resistances 
to  conduction  ?  From  what  do  the  resistances  chiefly  arise?  What  is 
the  law  for  the  resistance  of  the  metallic  parts  ?  What  lor  the  liquid  ? 
How  is  the  total  force  of  the  voltaic  battery  determined  ?  Describe  the 
apparatus,  Fig.  324. 


302  ELECTROTYPE. 

on  bringing  it  into  contact  again  the  action  is  re-establish- 
lished.  And  if  the  apparatus  is  in  a  dark  place  whenev- 
er d  is  lifted  from  either  plate,  z  or  c,  a  small  but  brilliant 
electric  spark  is  seen,  showing  therefore  that  electricity  is 
the  agent  at  work. 

If  the  gas  which  rises  from  the  copper  plate  be  exam- 
ined, it  turns  out  to  be  hydrogen,  and  the  corrosion  of  the 
zinc  is  due  to  the  combination  of  that  metal  with  oxygen. 
Water,  therefore,  must  have  been  decomposed  to  furnish 
these  elements.  The  electric  action  of  the  common  voltaic 
circle  arises  from  the  decomposition  of  water. 

If  the  wire  d  be  a  slender  piece  of  platinum  it  contin- 
ues in  an  ignited  condition  as  long  as  the  apparatus  is  in 
activity.  The  electricity  must,  therefore,  flow  in  a  contin- 
uous current ;  and,  as  the  most  powerful  voltaic  batteries 
are  nothing  but  combinations  of  these  simple  ones,  the 
same  reasoning  applies  to  both,  and  we  attribute  their  ac- 
tion to  the  same  cause — chemical  decompositions  going 
on  in  them,  and  giving  rise  to  an  evolution  of  electri- 
city which  flows  in  a  continuous  current  from  end  to  end 
of  the  instrument  and  back  through  its  polar  wires. 

A  very  beautiful  process  for  working  in  metals,  called 
the  electrotype,  and  founded  upon  the  principles  explain- 
ed in  this  lecture,  has  been  lately  introduced  into  the  arts. 
When  water  is  submitted  to  the  influence  of  a  voltaic 
current  we  have  seen  that  it  is  resolved  into  its  constitu- 
ent elements,  oxygen  and  hydrogen,  a  total  separation 
ensuing,  and  each  of  these  going  to  its  own  polar  wire. 
In  the  same  manner,  when  a  metalline  salt  transmits  the 
voltaic  current,  decomposition  ensues,  the  acid  part  of  the 
salt  being  evolved  at  the  positive  and  the  metalline  part 
at  the  negative  pole.  When  the  salt  has  been  properly 
selected  the  metal  is  deposited  as  a  coherent  mass,  and 
faithfully  copies  the  form  of  any  surface  in  which  the 
negative  pole  is  made  to  terminate.  Thus,  to  the  polar 
wire  Z,  Fig.  325,  of  a  simple  voltaic  battery  let  there 
be  attached  a  coin  or  other  object,  N,  one  surface  of 
which  has  been  varnished  or  covered  with  some  non- 


What  ensues  when  a  metallic  communication  is  made  between  the 
metals  ?  How  can  it  be  proved  that  electricity  is  concerned  in  these  re- 
sults ?  Why  do  we  know  that  water  must  have  been  decomposed  ?  Why 
do  we  know  that  there  is  a  continuous  current  of  electricity  passing  ?  On 
what  principles  is  the  electrotype  process  founded  ? 


ELECTROTYPE. 


303 


conducting  material ;  to  the  other  wire,  S,  let  there  be 
affixed  a  mass  of  copper,  C, 
and  let  the  trough,  N  C,  in 
•which  these  are  placed  be  filled 
with  a  solution  of  sulphate  of 
copper.  Now,  when  the  bat- 
tery is  charged,  the  sulphate  of 
copper  in  the  trough  undergoes 
decomposition,  metallic  copper 
being  deposited  on  the  face  of 
the  coin,  N  ;  and  as  this  with- 
drawal of  the  metal  from  the  so- 
lution goes  on,  the  mass,  C,  undergoes  corrosion,  and,  dis- 
solving in  the  liquid,  replaces  that  which  is  continually 
accumulating  on  the  face  of  the  coin.  When  the  experi- 
menter judges  that  the  deposit  on  N  is  sufficiently  thick,  he 
removes  it  from  the  trough,  and  with  the  point  of  a  knife 
splits  it  from  the  surface  of  the  coin.  The  cast  thus  ob- 
tained is  admirably  exact. 

In  the  same  manner  that  copper  may  thus  be  obtained 
from  the  sulphate,  so  other  metals  may  be  used.  Casts  in. 
gold  and  silver,  and  even  alloys,  such  as  brass,  may  be 
obtained.  There  is  no  difficulty  in  gilding,  silvering,  or 
platinizing  surfaces,  and  from  a  single  cast,  by  using  it 
in  turn  as  a  mould,  innumerable  copies  may  be  taken. 


Describe  one  of  the  methods  for  taking  casts.     Can  other  metals  be- 
sides copper  be  used  ?    Is  this  process  adapted  for  gilding  and  silvering  ? 


304 


ELECTRO-MAGNETISM. 


Fig.  326. 
A 


LECTURE  LXI. 

ELECTRO-MAGNETISM. — Action  of  a  Conducting  Wire  on 
tL"  Needle. —  Transverse  Position  assumed. — Effects  of 
a  Uent  Wire. —  The  Multiplier. — Astatic  Galvanometer. 
Electro-  Magnet. — Rotatory  Movements. — Attraction  and 
Repulsion  of  Currents. — Electro-Dynamic  Helix. — Elec- 
tro-Magnetic Theory. 

WHEN  a  magnetic  needle,  having  freedom  of  motion 
upon  its  center,  is  brought  near  a  wire  through  which 
an  electric  current  is  passing,  the  needle  is  deflected  and 
tends  to  move  into  such  a  position  as  to  set  itself  at  right 
angles  to  the  wire. 

Thus,  let  there  be  an  electric  cur- 
rent moving  in  the  wire  A  B,  Fig. 
326  :  in  the  direction  of  the  arrow, 
and  directly  over  the  wire  and  par- 
allel to  it,  let  there  be  placed  a  sus- 
pended needle  ;  as  soon  as  the  cur- 
rent passes  in  the  wire,  the  needle 
is  deflected  from  its  north  and  south 
position,  and  turns  round  transverse- 
ly, and  if  the  current  is  strong  enough 
the  needle  comes  at  right  angles  to 
the  wire. 

Now,  every  thing  remaining  as 
before,  let  the  current  pass  in  the 
opposite  direction,  the  deflection 
takes  place  as  before,  only  now  it  is  also  in  the  opposite 
direction. 

If  the  needle  be  placed  by  the  side  of  the  wire  the 
same  effect  is  observed.  On  one  side  it  dips  down  arid 
on  the  other  it  rises  up. 

What  effect  ensues  when  a  magnetic  needle  is  brought  near  a  conduct 
ing  wire?  How  may  it  be  proved  that  the  direction  of  the  motion  de 
pends  on  the  direction  of  the  current  ?  What  takes  place  when  the  nee 
die  is  at  the  side  of  the  wire  ? 


GALVANIC    MULTIPLIERS. 


305 


In  whatever  position  the  needle  is  placed  as  respects 
the  conducting  wire  it  tends  to  set  itself  at  right  angles 
thereto.  This  discovery  was  made  by  Oersted  in  1819. 

From  the  foregoing  experiments  it  will  appear  that  if 
a  wire  be  bent  into  the  Fig.  327. 

form  of  a  rectangle,  as 
represented  in  Fig.  327, 
and  an  electric  current 
be  made  to  flow  round 
it  in  the  direction  of  the 
arrows,  all  the  parts  of 
the  current  tend  to  move 
a  needle  in  the  interior 
of  such  a  rectangle  in  the  same  direction,  and,  therefore, 
it  will  be  much  more  energetically  disturbed  than  by  a 
single  straight  wire. 

If  the  wire,  instead  of  making  one  convolution  or  turn, 


Fig.  328. 


A  fine 


Fig.  329. 


is  bent  many  times  on  itself, 
so    that    the   same    current 
may  act  again  and  again  up- 
on the  needle,^ the  effect  of 
a  very  feeble  force  may  be 
rendered    perceptible.      On 
this  principle  the  galvanometer  is  constructed, 
copper   wire,  wrapped  with  silk,  is 
bent  on  itself  many  times,  forming 
a  rectangle,  d  d,  Fig.  328  ;  the  two 
projecting  ends,  a  a,  dip  into  mer- 
cury-cups, by  which  they    may  be 
connected    with  the   apparatus,  the 
electric   current  of  which  is  to  be 
measured.     In  the   interior  of  the 
rectangle,  supported  on  a  pivot,  is 
a  magnetic  needle,  n  s,  the  deflec- 
tions of  which  measure  the  current. 
A  still  more  delicate  instrument 
is  made  by  placing  two  needles,  with 
their  poles  reversed,  on  the  same 
axis,  N  S,  s  n,  suspending  them  by 
a  fine  thread  in  such  a  way  that  one 

By  whom  were  these  facts  discovered  ?  What  effect  is  there  on  a  nee- 
dle in  the  interior  of  a  rectangle  ?  What  is  the  effect  when  the  wire 
makes  many  convolutions?  Describe  the  deflecting  galvanometer. 


306 


ELECTRO-MAGNETS. 


of  the  needles  is  in  the  inside  of  the  rectangle  and  the 
other  above.  If  the  needles  are  of  equal  power  the  com- 
bination is  astatic — that  is,  not  under  the  magnetic  influ- 
ence of  the  earth  ;  but  both  of  them  are  moved  in  the 
same  direction  by  the  passage  of  the  current.  Such  an 
instrument  is  called  an  astatic  galvanometer. 

When  an  electric  current,  moving  in  a  wire,  is  made 
to  pass  round  a  piece  of  soft  iron,  so  long  as  the  current 
continues  the  iron  is  magnetic  ;  but  the  moment  the  cur- 
rent ceases  the  iron  loses  its  magnetism.  If,  therefore,  a 
bar  of  soft  iron  be  bent  into  the  form  N  S,  Fig.  330,  and 

Fig.  330. 

b 


there  be  wound  round  it  a  copper  wire  in  a  continuously 
spiral  course,  the  strands  of  the  wire  being  kept  from 
touching  one  another,  and  also  from  contact  with  the  iron, 
by  being  covered  with  silk,  whenever  a  current  is  passed 
through  the  wires  by  the  aid  of  the  binding-screws,  p  m, 
the  iron  becomes  intensely  magnetic.  The  amount  of  its 
magnetism  may  be  measured  by  attaching  the  keeper,  A, 
to  the  arm  of  a  lever,  a  b,  which  works  on  a  fulcrum,  c  ; 
Ti  is  a  hook  by  which  weights  may  be  suspended.  In  this 
way  magnets  have  been  made  which  would  support  more 
than  a  ton. 

Mr.  Faraday  discovered  that  rotatory  movements  could 
be  produced  by  magnets  round  conducting  wires ;  and, 
conversely,  that  conducting  wires  would  rotate  round 
magnets.  Both  these  facts  may  be  proved  at  once  by  the 
instrument  Fig.  331.  On  the  top  of  a  pillar,  gc,  a  strong 
copper  wire,  bent  as  in  the  figure,  at  d  f,  is  fastened. 

Describe  the  astatic  galvanometer.  How  may  transient  magnetism  be 
communicated  to  an  iron  bar  ?  Describe  the  instrument,  Fig.  330. 


ELECTRO-MAGNETIC    ROTATIONS.  307 

To  the  crook  aty* a  fine  platina  wire,  h,  hangs  by  a  loop, 
on  which  it  has  perfect  free- 
dom  of  motion.  Its  lower  end, 

jy,  on   which  is   a  small  glass  (Uf 

bead,  dips  under  some  mer- 
cury in  a  reservoir,  b,  in  the 
center  of  which  a  magnetiz- 
ed sewing-needle,  n,  is  fasten- 
ed by  means  of  a  slip  of  cop-  q 
per,  which  communicates  with 
the  binding-screw,  z.  On  the  arm,  d,  there  is  soldered 
inflexibly  another  platinum  wire,  e,  which  dips  into  a 
mercury  reservoir,  a,  which  is  in  metallic  connection 
with  the  binding-screw  c  by  means  of  a  slip  of  copper. 
From  the  center  and  bottom  of  this  reservoir  a  magnet- 
ized sewing-needle  is  fixed  by  means  of  thin  platinum 
wire,  so  as  to  have  freedom  of  motion  round  e.  Under 
these  circumstances,  if  an  electric  current  is  passed  from 
c  along  d,  in  the  direction  of  the  arrow,  to  z,  the  magnet, 
7tt,  rotates  round  the  fixed  wire  in  one  direction,  and  the 
wire,  k,  round  the  fixed  magnet  n  in  the  other.  On  re- 
versing the  course  of  the  current  these  motions  are  re- 
versed. 

On  similar  principles  all  kinds  of  rotatory,  reciproca- 
tory,  and  other  movements  may  be  accomplished,  magnets 
made  to  revolve  on  their  own  axes,  and  entire  galvanic 
batteries  round  the  poles  of  magnets. 

In  frictional  electricity  we  have  seen  that  the  funda- 
mental law  of  action  is,  that  like  electricities  repel  and 
unlike  ones  attract.  In  the  same  way  attractive  and 
repulsive  motions  have  been  discovered  in  the  case  of 
currents.  If  electric  currents  flow  in  two  wires  which 
are  parallel  to  each  other,  and  have  freedom  of  motion, 
the  wires  are  immediately  disturbed.  If  the  currents 
run  in  the  same  direction  the  wires  move  toward  each 
other,  if  in  the  opposite  the  wires  move  apart.  Or,  briefly, 
"  like  currents  attract,  and  unlike  ones  repel'' 

If  a  wire  be  coiled  into  a  spiral  form,  and  its  ends  car- 
ried back  through  its  axis,  as  shown  in  Fig.  332,  it  forms 

How  may  movements  of  rotation  of  wires  and  magnets  round  one 
another  be  shown?  Describe  the  instrument,  Fig.  331.  What  ensues  on 
reversing  the  current  1  What  is  the  action  of  currents  on  each  other  ? 
What  is  the  general  law  of  this  action  ? 


308  THEORY    OF    MAGNETISM. 

Fig.  332.  an  electro-dynamic  helix.     If  it  be  sus- 

pended with  freedom  of  motion  in  a 
horizontal  plane,  it  points  as  a  magnetic 
needle  would  ii&,  north  and  south ;  or  if 
suspended,  so  as  to  move  in  a  vertical 
plane,  it  dips  like  a  dipping-needle. 

All  the  properties  of  a  needle  may  be 
simulated  by  such  a  helix;  and  if  two  he- 
lices, carrying  currents,  are  presented  to 


each  other,  they  attract  and  repel,  under 
the   same  laws   that  two  magnetic  bars 


would  do. 

If,  therefore,  we  imagine  an  electric  current  to  circu- 
late round  a  magnet  transversely  to  its  axis,  such  a  sup- 
position will  account  for  all  its  singular  properties. 

Anticipating  what  will  have  to  be  said  presently  as  re- 
spects thermo-electricity,  it  may  be  observed,  that  if  we 
take  a  metal  ring,  and  warm  it  in  one  point  only,  by  a 
spirit-lamp,  no  effect  ensues  ;  but  if  the  lamp  is  moved 
an  electric  current  runs  round  the  wire  in  the  course  the 
lamp  has  taken. 

As  with  this  metal,  wire,  and  lamp,  so  with  the  earth. 
The  sun,  by  his  apparent  motion,  warms  the  parts  of  the 
earth  in  succession,  and  electric  currents  are  generated, 
which  follow  his  course.  We  must  now  call  to  mind  all 
that  has  been  said  respecting  the  influence  of  the  sun's 
heat  on  the  magnet,  in  Lecture  LVII.  This  elucidates 
the  cause  of  the  needle  pointing  north  and  south.  It 
comes  into  that  position  because  it  is  the  position  in  which 
the  electric  currents  in  it  are  parallel  to  those  in  the  earth. 
This  is  the  position,  as  has  just  been  explained,  that  cur- 
rents will  always  assume.  We  see  why,  at  the  polar  re- 
gions, it  dips  vertically  down.  It  is  again  that  its  currents 
may  be  parallel  with  those  of  the  earth  ;  for  in  those  re- 
gions the  sun  performs  his  daily  motion  in  circles  parallel 
to  the  horizon.  We  see,  also,  that  it  is  for  the  same  cause, 
in  intermediate  latitudes,  that  the  needle  points  north  and 
also  dips. 

What  is  an  electro-dynamic  helix  ?  When  two  such  helices  act  on  each 
other  what  phenomena  arise  ?  What  ensues  when  a  metal  ring  is  warm- 
ed at  one  point  by  a  lamp,  and  what  when  the  lamp  is  moved  ?  How  do 
these  facts  bear  on  the  polarity  and  dip  of  the  needle  ?  Why  does  a  mag-v 
netic  needle  point  north  and  south  ?  Why  does  it  dip  T 


MAGNETO-ELECTRICITY.  309 

This  prolific  theory  likewise  includes  all  the  phenom- 
ena of  Oersted,  such  as  the  transverse  position  a  needle 
takes  when  under  the  influence  of  a  conducting-wire  ;  for 
this  is  again  the  position  in  which  the  currents  of  the 
needle  are  parallel  to  that  in  the  wire. 


LECTURE  LXII. 

MAGNETO-ELECTRICITY.  —  THERMO-ELECTRICITY,  —  Pro- 
duction of  Electric  Currents  by  Magnets. — Momentary 
Nature  of  these  Currents. —  They  give  rise  to  Sparks, 
Decompositions,  fyc. — Magneto- Electric  Machines. — In- 
duction of  Currents  by  Currents. — Electro-Magnetic  Tel- 
egraph.— Production  of  Cold  and  Heat  by  Electric  Cur- 
rents.—  Thermo-electricity. — Melloni's  Multiplier. 

IF  an  electric  current  passing  round  the  exterior  of  a 
bar  ofjfsoft  iron  can  convert  it  into  a  magnet,  we  should 
expect  that  the  converse  would  hold  good,  and  a  magnet 
ought  to  be  able  to  generate  an  electric  current  in  a  con- 
ducting-wire. 

Let  there  be  a  helix  of  Fig.  333. 

copper  wire,  a,  Fig.  333, 
the  successive  strands  of 
which  are  kept  from 
touching,  and  let  its  ends 
at  b  be  brought  in  con- 
tact. If  a  bar  magnet, 
N  S,  is  introduced  in  the 
axis,  so  long  as  it  is  in 

actual  movement  an  electric  current  will  run  through  the 
wire,  but  as  soon  as  the  bar  comes  to  rest  the  current 
ceases.  On  withdrawing  the  bar  the  current  again  flows, 
but  now  it  flows  in  the  opposite  direction. 
•  If,  therefore,  we  alternately  introduce  and  remove  with 
rapidity  a  steel  magnet,  opposite  currents  will  inces- 
santly run  round  the  helix.  If  we  open  the  wire  at  the 
point  b,  every  time  the  current  passes  a  bright  spark  is 

How  does  this  theory  include  Oersted's  phenomena  ?  Can  a  magnet 
develop  electric  currents  in  a  wire  ?  Under  what  circumstances  does  this 
take  place  ?  How  long  does  the  current  continue  ?  Describe  the  instru- 
ment, Fig.  333. 


310  MAGNETO-ELECTRIC    MACHINE. 

seen  ;  or  if  the  two  separated  ends  dip  into  water  it  un- 
dergoes decomposition. 

Fig.  334.  The  same  results  would,  of  course, 

occur,  if,  instead  of  introducing  and 
removing  a  permanent  steel  magnet, 
we  continually  changed  the  polarity 
of  a  stationary  soft  iron  bar.  Thus 
if  a  b,  Fig.  334,  be  a  rod  of  soft  iron, 
surrounded  by  a  helix,  and  there  be 
taken  a  semicircular  steel  magnet, 
N  c  S,  which  can  be  made  to  revolve 
on  a  pivot  at  c — things  being  so  ar- 
ranged that  its  poles,  N  and  S,  in 
their  revolutions,  just  pass  by  the  terminations  of  the  bar, 
a  b — the  polarity  of  this  bar  will  be  reversed  every  half 
revolution  the  magnet  makes,  and  this  reversal  of  polari- 
ty will  generate  electric  currents  in  the  wire.  To  instru- 
ments constructed  on  these  principles  the  name  of  mag- 
neto-electric machines  is  given. 

The  peculiarity  of  these  currents  is  their  momentary 
duration.  Hence  they  have  been  called  momentary  cur- 
rents, and  from  the  name  of  their  discoverer,  Faradian 
currents. 

There  are  a  great  many  different  forms  of  magneto- 
electric  machines.  In  some,  permanent  steel  magnets  are 
employed;  in  others,  temporary  soft  iron  ones,  brought 
into  activity  by  a  voltaic  battery. 

Fig.  335  represents  Saxton's  magneto-electric  machine. 
It  consists  of  a  horse-shoe  magnet,  A  B,  laid  horizontally. 
The  keeper,  C  D,  is  wound  round  with  many  coils  of 
wire,  covered  with  silk.  It  rotates  on  an  axis,  E  F,  on 
which  it  is  fixed,  by  means  of  a  pulley  and  multiplying- 
wheel,  E  G.  The  terminations  of  the  wire,  li  i,  dip  into 
mercury  cups  at  K.  When  the  wheel  is  set  in  motion 
the  keeper  rotates,  its  polarity  being  reversed  every  half 
turn  it  makes  before  the  magnet,  and  momentary  currents 
run  through  its  wires. 

If  it  is  desirable  to  give  the  current  of  a  magneto-elec- 
tric machine  great  intensity,  so  as"  to  furnish  powerful 
shocks,  or  effect  decompositions,  the  wire  which  is  wound 

What  are  magneto-electric  machines  ?  What  names  have  their  cur- 
rents received  ?  Describe  Saxton's  magneto-electric  machine.  What  is 
the  effect  of  using  a  long  thin  and  short  thick  wire  ? 


INDUCTION  OF  CURRENTS  BY  CURRENTS. 


311 


round  the  keeper  should  be  thin  and  long  ;  hut  for  pro- 
ducing incandescence  in  metals,  or  for  sparks  or  magnet- 
ic operations,  the  wire  should  be  short  and  thick. 


Fig.  335. 


hi? 


Admitting  the  theory  that  all  magnetic  action  arises 
from  the  passage  of  electrical  currents,  it  follows,  from  the 
facts  just  detailed,  that  an  electrical  current  must  have 
the  power  of  inducing  others  in  conducting  bodies  in  its 
neighborhood.  Experiment  proves  that  this  conclusion 
is  correct,  and  currents  so  arising  are  called  induced  or 
secondary  currents. 

Thus,  when  two  wires  are  extended  parallel  to  one  an- 
other, and  through  one  of  them  an  electric  current  is 
passed,  a  secondary  current  is  instantly  induced  in  the 
other;  but  its  duration  is  only  momentary.  It  flows  in 
the  opposite  direction  to  the  primary  one.  On  stopping 
the  primary  current,  induction  again  takes  place  in  the 
secondary  wire ;  but  the  current  now  arising  has  the  same 
direction  as  the  primary  one.  The  passage  of  an  electri- 
cal current,  therefore,  develops  other  currents  in  its 
neighborhood,  which  flow  in  the  opposite  direction  as  the 

How  may  it  be  proved  that  electric  currents  induce  others  in  their  neigh- 
borhood ?  What  direction  does  the  induced  current  take  at  first,  and 
what  at  last? 


312 


MAGNETIC    TELEGRAPH. 


primary  one  first  acts,  but  in  the  same  direction  as  it 
ceases. 

Morse's  electro-magnetic  telegraph  is  essentially  a  horse- 
shoe of  soft  iron,  made  temporarily  magnetic  by  the  pass- 
age of  a  voltaic  current.  In  Fig.  336,  m  m  represent 

Fig.  336. 


the  poles  of  the  magnet,  wound  round  with  wire ;  at  a  is 
a  keeper,  which  is  fastened  to  a  lever,  a  I,  which  works 
on  a  fulcrum,  at  d;  the  other  end  of  the  lever  bears  a 
steel  point,  ,?,  which  serves  as  a  pen.  At  c  is  a  clock  ar- 
rangement for  the  purpose  of  drawing  a  narrow  strip  of 
paper,  p  p,  in  the  direction  of  the  arrows.  W  W  are  the 
wires  which  communicate  with  the  distant  station.  As 
soon  as  a  voltaic  current  is  made  to  pass  through  these 
wires,  the  soft  iron  becomes  magnetic,  and  draws  the 
keeper,  a,  to  its  poles ;  and  the  other  end  of  the  lever,  I, 
rising  up,  the  point  s  is  pressed  against  the  moving  paper 
and  makes  a  mark.  When  the  lever  first  moves  it  sets 
the  clock  machinery  in  motion,  and  the  bell,  Z»,  rings  to 
give  notice  to  the  observer.  When  the  distant  operator 
stops  the  current,  the  magnetism  of  m  m  ceases,  and  the 
keeper,  a,  rising,  *  is  depressed  from  the  paper.  By  let- 
ting the  current  flow  round  the  magnet  for  a  short  or  a 
longer  time  a  dot  or  a  line  is  made  upon  the  paper — and 

Describe  Morse's  telegraph.    How  are  the  dots  and  lines  which  com* 
pose  the  telegraphic  alphabet  made  by  the  machine  ? 


THERMO-ELECTRICITY".  313 

the  telegraphic  alphabet  consists  of  such  a  series  of  marks. 
It  is  not  necessary  to  use  two  wires  to  the  instrument ;  one 
alone  is  commonly  employed  to  carry  the  current  to  the 
magnet ;  it  is  brought  back  through  the  earth. 

If  a  bar  of  bismuth,  b,  Fig.  337,  and  one  of  antimony, 
«,  be  soldered  together  at  the  point  c,  and  by       Fig.  337. 
means  of  wires  attached  to  the  other  ends,  a 
feeble  voltaic  current  is  passed  from  the  an- 
timony to  the  bismuth,  heat  will  be  genera- 
ted at  the  junction,  c;  but  if  the  current  is 
made  to  pass  from  the  bismuth  to  the  anti- 
mony, cold  is  produced,  so  that  if  an  excava- 
tion be  made  at  c,  and  a  little  water  intro- 
duced in  it  it  may  be  frozen. 

The  converse  of  this  also  holds  good.  If  we  connect 
the  free  terminations  of  a  arid  b,  by  means  of  a  wire,  and 
raise  the  temperature  of  the  junction  c,  an  electric  cur- 
rent sets  from  the  bismuth  to  the  antimony;  but  if  we 
cool  the  junction  the  current  sets  in  the  opposite  way. 
To  these  currents  the  name  of  thermo-electric  currents  is 
given. 

Thermo-electric  currents,  from  the  circumstance  that 
they  originate  in  good  conductors,  possess  but  very  little 
intensity.  They  are  unable  to  pass  through  the  thinnest 
film  of  water,  and,  therefore,  in  operating  with  them  it  is 
necessary  that  all  the  parts  of  the  apparatus  through  which 
they  are  to  flow  should  be  in  perfect  metallic  contact. 
The  slightest  film  of  oxide  upon  a  wire  is  sufficient  to 
prevent  their  entrance  into  it. 

As  the  effects  of  the  voltaic  circle  can  be  increased  by 
increasing  the  number  of  pairs  forming  it,  the  same  is  also 
true  for  thermo-electric  currents.  Thus,  if  we  take  a  se- 
ries of  bars  of  bismuth  and  antimony,  and  solder  their 
alternate  ends  to  one  another,  as  shown  pig.  338. 

in  Fig.  338,  on  warming  one  set  of  the    5    5    j    &     &     a, 
junctions,  the   current  passes,   and   is  \f\f\f\/\/J 
greater  in  force  according  as  the  num-    \/\/\/\/\/ 
ber  of  alternations  warmed  is  greater.       a    a    a    a,    a 

From  their  feeble  intensity,  these  currents,  when  passed 
through  the  wire  of  a  multiplying  galvanometer,  Fig.  329, 

What  effects  arise  from  passing  feeble  electric  currents  through  a  pair 
of  bars  of  bismuth  and  antimony  ?  What  are  thermo-electric  currents  ? 
Why  have  they  so  little  intensity  ?  How  may  that  intensity  be  increased? 

o 


314  THERMO-MULTIPLIER. 

do  not  give  rise  to  the  same  effects  that  are  observed  in 
ordinary  voltaic  currents — they  lose  as  much  of  their  force 
by  the  resistance  to  conduction  of  the  slender  wire  as  they 
gain  by  the  effect  which  each  coil  impresses  on  the  nee- 
dle. A  multiplier,  suited  for  thermo-electric  currents, 
should  be  made  of  stout  wire,  and  make  but  few  turns 
round  the  needle. 

Melloni's   thermo-electric  pile  is  represented  in  Fig. 
339.     It  consists  of  thirty  or  forty  pairs  of  small  bars  of 

Fig.  339. 

1C       A 


bismuth  and  antimony,  with  their  alternate  ends  soldered 
together,  forming  a  bundle,  F  F.  The  polar  wires,  C  C, 
projecting,  are  put  in  communication  with  the  multiplier. 
To  each  end  of  the  pile  brass  caps,  as  seen  in  the  figure, 
fit.  These  serve  to  cut  off  the  disturbing  influence  of 
currents  of  air;  and  now  if  the  hand  or  any  other  source 
of  heat  be  presented  to  one  side  of  the  pile,  the  needle 
of  the  galvanometer  immediately  moves,  and  the  amount 
of  its  deflection  increases  with  the  temperature  of  the 
radiant  source. 

It  is  not  necessary  to  use  many  alternations,  as  in  the 
instrument  of  Melloni.     Let  a  pair  of  heavy  bars    Fig.  340. 
of  bismuth  and  antimony,  of  the  shape  repre- 
sented in  Fig.  340,  be  soldered  by  the  edges, 
a  b,  to  a  circular  plate  of  thin  copper,  and  at 
the  others  at  a'  b',  to  semicircular  plates,  e  f, 
having  projecting  pieces  to  communicate   with 
the  wire  of  a  galvanometer  of  few  convolutions, 
and  the  needle  of  which  is  nearly  astatic.    It  will 
be  found  that  extremely  minute  changes  of  temperature 
may  be  indicated — the  combination  answering  very  well 
instead  of  Melloni's  more  costly  instrument. 

Why  does  not  the  common  galvanometer  increase  the  effect  of  these 
currents  ?  What  ought  to  be  the  construction  of  a  thermo-electric  multi- 
plier ?  Describe  Melloni's  instrument.  Is  it  necessary  to  use  so  many  al- 
ternations ? 


ASTRONOMY.  315 


ASTRONOMY. 


LECTURE  LXIII. 

ASTRONOMY. —  TJie  Figure  of  the  Earth. —  The  Earth  Ro- 
tates on  her  Axis. — Illustrations  of  Diurnal  Rotation. — 
Annual  Translation  round  the  Sun. —  The  Year. — Mo- 
tions of  the  Moon. — Planets  and  Comets. — Astronomical 
Definitions. 

IN  the  infancy  of  knowledge  the  first  impression  which 
men  entertained  respecting  the  form  of  the  earth  we  in- 
habit, was  that  it  is  an  indefinitely-extended  plane,  the 
more  central  portions  being  the  land,  surrounded  on  all 
sides  by  an  unknown  expanse  of  sea.  Many  natural  phe- 
nomena soon  corrected  these  primitive  ideas,  and  almost 
as  far  back  as  historic  records  reach,  philosophers  had 
come  to  the  conclusion  that  our  earth  in  reality  is  of  a 
round  or  globular  form. 

To  this  conclusion  a  consideration  of  the  daily  phenom- 
ena of  the  starry  firmament  would  naturally  lead.  Every 
evening  we  see  the  stars  rising  in  the  east,  and  as  the 
night  goes  on,  passing  over  the  vault  of  the  sky,  and  at 
last  setting  in  the  west.  During  the  day  the  same  is  also 
observed  as  respects  the  sun.  And  as  these  are  events 
which  are  taking  place  day  after  day,  in  succession,  and 
no  man  can  doubt  that  the  objects  which  we  see  to-day 
are  those  which  we  saw  yesterday,  it  necessarily  follows, 
that  after  they  have  sunk  under  the  western  horizon,  they 
pursue  their  paths  continuously,  and  that  the  earth  neither 
extends  indefinitely  in  the  horizontal  direction,  nor  verti- 
cally downward,  but  that  she  is  of  limited  dimensions  on 
all  sides. 

What  was  probably  the  primitive  idea  respecting  the  figure  of  the  earth  ? 
How  may  it  be  proved  that  the  earth  is  limited  on  all  sides  T 


316  FIGURE    OF    THE    EARTH. 

Where  the  prospect  is  uninterrupted,  as  at  sea,  we  are 
further  able  not  only  to  verify  the  foregoing  conclusion, 
but  also  to  obtain  a  clearer  notion  of  the  figure  of  the 
earth.  Thus,  as  is  seen  in  Fig.  341,  let  an  observer  be 

Ffr.341. 


watching  a  ship  sailing  toward  him  at  sea.  When  she  is 
at  a  great  distance,  as  at  a,  he  first  perceives  her  topmast, 
but  as  she  approaches  from  a  toward  b,  more  and  more 
of  her  masts  come  into  view,  and  finally  her  hull  appears. 
When  she  arrives  at  b  she  is  entirely  visible.  Now,  as 
this  takes  place  in  whatever  direction  she  may  approach, 
whether  from  the  north,  south,  east,  or  west,  it  obviously 
points  out  the  globular  figure  of  the  earth.  In  the  distant 
position,  more  or  less  of  the  ship  is  obscured  by  the  in- 
tervening convexity — a  phenomenon  which  never  could 
take  place  were  the  earth  an  extended  plane. 

This  great  truth,  though  admitted  by  philosophers  in 
ancient  times,  fell  gradually  into  disrepute  during  the 
middle  ages  ;  it  was  re-established  at  the  restoration  of 
learning  only  after  a  severe  struggle.  It  is  now  the  basis 
of  modern  astronomy. 

The  spheroidal  figure  being  therefore  received  as  a 
demonstrated  fact,  it  is  next  to  be  observed  that  the  earth 
is  not  motionless  in  space,  but  in  every  twenty-four  hours 
turns  round  once  upon  her  axis.  That  such  a  motion  ac- 
tually occurs  is  clear  from  the  fact  of  the  rising  and  set- 
ting of  the  celestial  bodies. 

To  an  observer  at  the  equator,  the  stars  rise  in  the 
eastern  horizon  and  set  in  the  western,  continuing  in  view 
for  twelve  hours,  and  being  invisible  for  twelve.  At  the 

What  facts  prove  that  she  is  of  a  round  or  globular  form  ?  When  was 
the  globular  form  of  the  earth  denied,  and  when  finally  established  ?  Has 
the  earth  a  motion  on  her  axis  ?  In  what  time  is  it  performed  ?  What 
are  the  phenomena  of  the  rising  and  setting  of  the  stars  at  the  equator 
and  the  poles? 


MOTION    OF    THE    SUN    AND    MOON.  317 

pole  the  rising  or  setting  of  a  star  is  a  phenomenon  never 
seen  ;  but  these  heavenly  bodies  seem  to  pursue  paths 
which  are  parallel  to  the  horizon.  In  intermediate  lati- 
tudes a  certain  number  of  stars  never  rise  or  set,  while 
others  exhibit  that  appearance.  In  any  of  these  posi- 
tions in  our  hemisphere  the  motion  of  the  heavens  seems 
to  be  round  one,  or,  rather,  two  points,  situated  in  opposite 
directions;  to  one  of  them  the  name  of  the  north,  and  to 
the  other  of  the  south  pole  is  given.  These  are  the 
points  to  which  the  poles  of  the  earth  are  directed. 

When  observations  are  made  for  some  days  or  months 
in  succession,  we  find  that  there  are  motions  among  the 
celestial  bodies  themselves  which  require  to  be  account- 
ed for.  First,  we  observe  that  the  sun  does  not  remain 
stationary  in  a  fixed  position  among  the  stars,  but  that  he 
has  an  apparent  motion  ;  and  that  after  the  lapse  of  a 
little  more  than  three  hundred  and  sixty-five  days  he  comes 
round  again  to  his  original  place.  As  with  the  diurnal 
motion  so  with  this  annual.  Consideration  soon  satisfies 
us  that  it  is  not  the  sun  which  is  in  movement  round  the 
earth,  but  the  earth  which  is  in  movement  round  the  sun. 
To  the  period  which  she  occupies  in  completing  this  rev- 
olution the  name  of  the  year  is  given.  Its  true  length  is 
three  hundred  and  sixty-five  days,  five  hours,  forty-eight 
minutes,  forty-nine  seconds. 

The  sun  seems,  in  his  daily  motion,  to  accompany  the 
stars  ;  but  if  we  mark  the  point  upon  the  horizon  at 
which  he  rises  or  sets  we  find  that  it  differs  very  much 
for  different  times  of  the  year.  The  same  observation 
may  be  made  by  observing  the  length  of  the  shadow  of 
an  upright  pole  or  gnomon  at  midday.  Such  observa- 
tions show  that  there  is  a  difference  in  his  meridian  alti- 
tude in  winter  and  summer  of  forty-seven  degrees. 

The  observation  of  a  single  night  satisfies  us  that  the 
moon  has  a  motion  of  her  own  round  the  earth.  It  is  ac- 
complished in  twenty-seven  days,  seven  hours,  and  forty 
three  minutes,  and  is  called  her  periodical  revolution ; 
but,  during  this  time,  the  earth  has  moved  a  certain  dis- 
tance in  the  same  direction — or,  what  is  the  same  thing, 
the  sun  has  advanced  in  the  ecliptic,  and  before  the  moon 
overtakes  him,  twenty-nine  days,  twelve  hours,  and  forty- 

What  other  motion  besides  this  may  be  discovered  '(  What  is  the  year  ? 
What  is  the  month  ? 


318  DEFINITIONS. 

four  minutes  elapse.  This,  therefore,  is  termed  her  synod- 
ical  revolution,  or  one  month. 

There  are  also  certain  stars,  some  of  which  are  re- 
markable for  their  brilliancy,  which  exhibit  proper  mo- 
tions. To  these  the  name  of  planets  is  given.  And  at 
irregular  intervals,  and  moving  in  different  directions 
through  the  sky,  there  appear  from  time  to  time  comets. 
Multitudes  of  these  are  telescopic,  though  some  have  ap- 
peared of  enormous  magnitude. 

There  are  several  technical  terms  used  in  astronomy 
which  require  explanation. 

By  the  celestial  sphere  we  mean  a  sky  or  imaginary 
sphere,  the  center  of  which  is  occupied  by  the  earth.  On 
it,  for  the  purposes  of  astronomy,  we  imagine  certain 
points  and  fixed  lines  to  exist. 

Those  circles  whose  planes  pass  through  the  center  of 
the  sphere  are  called  great  circles.  The  circumference  of 
each  is  divided  into  three  hundred  and  sixty  parts,  called 
degrees,  and  marked  (°),  each  degree  into  sixty  minutes, 
marked  ('),  and  each  minute  into  sixty  seconds,  marked  ("). 

All  great  circles  bisect  each  other. 

Less  circles  are  those  whose  planes  do  not  pass  through 
the  center  of  the  sphere. 

The  axis  of  the  earth  is  an  imaginary  line,  drawn  through 
her  center,  on  which  she  turns.  The  extremities  of  this 
line  are  the  poles. 

A  line  on  the  earth's  surface  every  where  equidistant 
from  the  poles  is  the  equator.  Circles  drawn  on  the  sur- 
face parallel  to  the  equator  are  called  simply  parallels, 
arid  sometimes  parallels  of  latitude. 

At  sea,  or  where  the  prospect  is  unobstructed,  the  sky 
seems  to  meet  the  earth  in  a  continuous  circle  all  round. 
To  this  the  name  of  sensible  horizon  is  given.  The  ra- 
tional horizon  is  parallel  to  the  sensible,  and  in  a  plane 
which  passes  through  the  center  of  the  earth. 

That  point  of  the  celestial  sphere  immediately  overhead 
is  the  zenith,  the  opposite  point  is  the  nadir. 

A  circle  drawn  through  the  two  poles  and  passing 
through  the  north  and  south  points  of  the  horizon  is  a 

What  are  the  planets  ?  What  are  comets  ?  What  is  the  celestial 
sphere  ?  What  are  great  and  less  circles  ?  What  is  the  axis  of  the  earth  ? 
What  are  the  poles,  the  equator,  and  parallels  of  latitude  ?  What  is  the 
sensible  and  what  the  rational  horizon  ?  What  is  the  zenith  and  the  nadir  ? 


DEFINITIONS.  319 

meridian.  Hour  circles  are  other  great  circles  which  pass 
through  the  poles. 

A  circle  drawn  through  the  zenith  and  the  east  and 
west  points  of  the  horizon  is  the  prime  vertical.  Other 
great  circles  passing  through  the  zenith  are  vertical  circles 
or  circles  of  azimuth. 

The  altitude  of  a  body  above  the  horizon  is  measured 
in  degrees  upon  a  vertical  circle.  As  the  zenith  is  90° 
from  the  horizon,  the  altitude  deducted  from  90°  gives 
the  zenith  distance. 

The  azimuth  of  a  body  is  its  distance  from  the  north 
or  south  estimated  on  the  horizon,  or  by  the  arc  of  the 
horizon  intercepted  between  a  vertical  circle  passing 
through  the  body  and  the  meridian. 

The  latitude  of  a  place  is  the  altitude  at  that  place  of 
the  pole  above  the  horizon,  or,  what  is  the  same  thing, 
the  arc  of  the  meridian  between  the  zenith  of  the  place 
and  the  equator.  At  the  earth's  equator  the  pole  is, 
therefore,  in  the  horizon ;  at  the  pole  it  is  in  the  zenith. 

The  longitude  of  a  place  on  the  earth  is  the  arc  of  the 
equator  intercepted  between  the  meridian  of  that  place 
and  that  of  another  place  taken  as  a  standard.  The 
observatory  of  Greenwich  is  the  standard  position  very 
commonly  assumed.  The  longitude  of  a  star  is  the  arc 
of  the  ecliptic  intercepted  between  that  star  and  the  first 
point  of  Aries. 

The  latitude  of  a  star  is  its  distance  from  the  ecliptic, 
measured  on  a  great  circle  passing  through  the  pole  of 
the  ecliptic  and  the  star. 

The  declination  of  a  heavenly  body  is  the  arc  of  an 
hour  circle  intercepted  between  it  and  the  equator. 

The  ecliptic  is  the  apparent  path  which  the  sun  de- 
scribes among  the  stars.  It  is  a  great  circle  which  cuts 
the  equator  in  two  points,  called  the  equinoxial  points, 
because  when  the  sun  is  in  those  points  the  nights  and 
days  are  equal ;  one  is  the  vernal,  the  other  the  autumnal 
equinox.  From  this  circumstance  the  equator  itself  is 
sometimes  called  the  equinoxial  line. 

What  is  a  meridian  ?  What  are  hour  circles  ?  What  is  the  prime  ver- 
tical ?  What  are  circles  of  azimuth  ?  What  are  altitude  and  zenith 
distance  ?  What  azimuth,  the  latitude  of  a  place,  and  the  declination  of 
a  heavenly  body  ?  What  is  the  longitude  of  a  place  and  that  of  a  star? 
What  is  the  ecliptic  ? 


320  DEFINITIONS. 

Two  points  on  the  ecliptic,  90°  distant  from  the  equi- 
noxial  points,  are  the  solstitial  points.  When  the  sun  is 
in  one  of  these  it  is  midsummer,  in  the  other  midwinter. 

Motions  in  the  direction  from  west  to  east  are  direct. 
Retrograde  motions  are  those  from  east  to  west. 

The  ecliptic  is  divided  into  twelve  equal  parts  called 
signs.  They  bear  the  following  names  and  have  the 
following  signs. 

Aries      CP  Libra 

Taurus   b  Scorpio          HI 

Gemini  rj  Sagittarius     / 

Cancer  25  Capricornus  V? 

Leo        si  Aquarius        ~ 

Virgo     n  Pisces  X 

Formerly  these  signs  coincided  with  the  constellations 
of  the  same  name,  but  owing  to  the  precession  of  the 
equinoxes,  to  be  described  hereafter,  this  has  ceased  to 
be  the  case. 

Two  parallels  to  the  equator — one  for  each  hemisphere 
— which  touch  the  ecliptic,  are  called  tropics.  That  for 
the  northern  hemisphere  is  the  tropic  of  Cancer  ;  that  for 
the  south  the  tropic  of  Capricorn.  Two  other  parallels — 
one  for  each  hemisphere — as  far  from  the  poles  as  the 
tropics  are  from  the  equator,  are  the  polar  circles,  the 
northern  one  is  the  arctic,  the  southern  one  the  antarctic. 

The  right  ascension  of  a  heavenly  body  is  the  distance 
intercepted  on  the  equator  between  an  hour  circle  passing 
through  it  and  the  vernal  equinoxial  point. 

The  astronomical  day  begins  at  noon,  the  civil  day  at 
midnight.  Both  are  divided  into  twenty-four  hours,  each 
hour  into  sixty  minutes,  each  minute  into  sixty  seconds. 

By  the  orbit  of  a  body  is  meant  the  path  it  describes. 
This,  in  most  cases,  is  an  ellipse. 

The  nodes  are  those  points  where  the  orbit  of  a  planet 
intersects  the  ecliptic.  The  ascending  node  is  that  from 
which  the  planet  rises  toward  the  north,  the  descending 
that  from  which  it  descends  to  the  south;  a  line  joining 
the  two  is  the  line  of  the  nodes. 

What  are  the  equinoxial  and  solstitial  points?  What  are  direct  and 
retrograde  motions  ?  How  is  the  ecliptic  divided  ?  What  are  the  tropics 
and  polar  circles?  What  is  right  ascension?  What  is  the  difference 
between  the  astronomical  and  civil  day?  What  is  an  orbit?  What  are 
the  ascending  and  descending  nodes  ? 


MOTION    OF    THE    SUN.  321 


LECTURE  LXIV. 

TRANSLATION  OP  THE  EARTH  ROUND  THE  SUN,  AND  ITS 
PHENOMENA. — Apparent  Motion  and  Diameter  of  the 
Sun. — Elliptical  Motion  of  the  Earth. — Sidereal  Year. 
— Determination  of  the  Sun's  Distance. —  Parallax. — 
Dimensions  of  the  Sun. —  Center  of  Gravity  of  the  Two 
Bodies. — Phenomena  of  the  Seasons. 

IN  the  last  lecture  it  has  been  observed  that  the  sun 
has  an  apparent  motion  among  the  stars  in  a  path  called 
the  ecliptic.  A  line  joining  that  body  with  the  earth,  and 
following  his  motions,  would  always  be  found  in  the 
same  plane,  or,  at  all  events,  not  deviating  from  that 
position  by  more  than  a  single  second. 

Observation  soon  assures  us  that  if  we  carefully  ex- 
amine the  rate  of  the  sun's  motion  in  right  ascension,  it  is 
far  from  being  the  same  each  day.  This  want  of  uni- 
formity might,  to  some  extent,  be  accounted  for  by  the 
obliquity  of  the  ecliptic;  but  even  if  we  examine  the 
motion  in  the  ecliptic  itself,  the  same  holds  good.  The 
sun  moves  fastest  at  the  end  of  the  month  of  December, 
and  most  slowly  in  the  end  of  June. 

Further,  if  we  measure  the  apparent  diameter  of  the  sun 
at  different  periods  of  the  year,  we  find  that  it  is  not  always 
the  same.  At  the  time  when  the  motion  just  spoken  of 
is  greatest,  that  is  during  the  month  of  December,  the 
diameter  is  also  greatest ;  and  when  in  June  the  motion 
is  slowest,  the  diameter  is  smallest.  These  facts,  there- 
fore, suggest  to  us  at  once  that  the  distance  between  the 
earth  and  the  sun  is  not  constant ;  but  in  December  it  is 
least,  and  in  June  greatest,  for  the  difference  in  size  can 
plainly  be  attributable  to  nothing  else  but  difference  of 
distance. 

The  annual  motion  of  the  sun  in  the  heavens,  like  his 
diurnal  motion,  is,  however,  only  a  deception.  It  is  not 

Does  the  sun  move  with  apparently  equal  velocity  each  day  ?  When  is 
his  motion  fastest  and  when  slowest  ?  Is  the  sun  always  of  the  same 
size  ?  When  is  he  largest  and  when  smallest  ?  How  can  we  be  certain 
that  the  earth  does  not  move  in  a  circle  round  the  sun  ? 


322 


MOTION    OF    THE    EARTH. 


the  sun  which  moves  round  the  earth,  but  the  earth  which 
has  a  movement  of  translation  round  the  sun,  as  well  as 
one  upon  her  own  axis.  The  path  which  she  thus  de- 
scribes is  not  a  circle,  for  in  that  case,  being  always  at 
the  same  distance,  the  sun  would  always  be  of  the  same 
apparent  magnitude,  and  his  motion  always  uniform ;  but 
it  is  an  ellipse,  having  the  sun  in  one  of  its  foci.  Thus, 
in  Fig.  342,  let  F  be  the  sun,  A  D  B  E  the  elliptic  orbit  of 
the  earth;  it  is  obvious  that  as  she  moves  in  this  path 

Fig.  342, 


she  will  be  much  nearer  the  focus  F  occupied  by  the  sun 
when  she  arrives  at  A  than  when  she  is  at  B.  To  the 
former  point,  therefore,  the  name  of  perihelion,  and  to 
the  latter  of  aphelion  is  given  ;  the  line  A  B  joining  them 
is  called  the  line  of  the  apsides. 

The  periodic  time  occupied  in  one  complete  revolution 
is  called  the  sidereal  year.  Its  length  is  365  days,  6  hours, 
9  minutes,  ll£  seconds. 

The  law  which  regulates  the  velocity  of  motion  of  the 
earth  round  the  sun  was  discovered  by  Kepler.  It  has 
already  been  explained,  in  speaking  of  central  forces,  in 
Lecture  XXI.  It  is  "  the  radius  vector  (that  is,  the  line 

How  do  we  know  it  is  in  an  ellipse  ?  What  are  the  perihelion  and  aphe- 
lion points  ?  What  is  the  line  of  the  apsides  ?  What  is  the  sidereal  year? 
What  is  Kepler's  law  respecting  the  radius  vector  ? 


PARALLAX. 


323 


Fig.  343. 


joining  the  centers  of  the  sun  and  earth)  sweeps  over 
equal  areas  in  equal  times." 

With  these  general  ideas  respecting  the  nature  of  the 
orbit  described  by  the  earth,  we  proceed,  in  the  next 
place,  to  the  determination  of  the  actual  size  of  that  orbit: 
in  other  words,  to  ascertain  the  distance  between  the  earth 
and  the  sun. 

Let  C,  Fig.  343,  be  the  center  of  the  earth,  B  the  po- 
sition of  an  observer  upon  it, 
and  M  the  sun ;  the  observer, 
B,  will  see  the  sun  in  the  direc- 
tion B  M,  and  refer  him  in  the 
heavens  to  the  position,  ».  An 
observer  at  C,  the  center  of  the 
earth,  would  see  him  in  the  po- 
sition C  M,  and  refer  him  to 
the  point  m.  His  apparent 
place  in  die  sky,  will,  therefore, 
be  different  i»  the  two  instances. 
This  difference  is  called  par- 
allax ;  and  a  little  consideration  shows  that  the  amount 
of  parallax  differs  with  the  place  of  observation  and  posi- 
tion of  the  body  observed,  being  greatest  under  the  cir- 
cumstances just  supposed,  when  the  body  is  seen  in  the 
horizon,  and  becoming  0  when  the  body  is  in  the  zenith. 
This  diminution  of  the  parallax  is  exemplified  by  sup- 
posing the  sun  at  M' ;  the  observer  at  B  refers  him  to  ri, 
the  observer  at  C  to  mf,  but  the  angle  B  M'  C  is  less  than 
the  angle  B  M  C.  Again,  if  the  sun  be  at  M" — that  is, 
in  the  zenith — both  observers,  at  B  and  C,  refer  him  to 
m",  and  the  parallax  is  0.  The  horizontal  parallax  being 
measured  by  the  angle,  B  M  C  is  evidently  the  angle  un- 
der which  the  semidiameter  of  the  earth  appears,  as  seen 
in  this  instance  from  the  sun. 

Although  we  cannot  have  access  to  the  center  of  the 
earth,  there  are  many  ways  by  which  the  parallax  may  be 
ascertained,  the  result  of  the  most  exact  of  which  has 
fixed  for  the  angle  BMC  the  value  of  about  eight  sec- 
onds and  a  half.  Now  it  is  a  very  simple  trigonometrical 
problem,  knowing  the  value  of  this  angle,  and  the  length 

What  is  parallax  ?  Why  does  the  parallax  become  0  in  the  zenith  ? 
What  is  the  horizontal  parallax  in  reality  ?  What  is  the  exact  value  of 
the  parallax  ? 


324  DISTANCE    AND    SIZE    OF    THE    SUN. 

of  the  line  B  C  in  miles,  to  determine  the  line  C  M.  When 
the  calculation  is  made,  it  gives  about  95,000,000  miles. 
This,  therefore,  is  the  mean  distance  of  the  earth  from 
the  sun. 

Knowing  the  apparent  diameter  of  an  object,  and  its 
distance  from  us,  we  can  easily  determine  its  actual  mag- 
nitude. Seen  from  the  earth,  the  sun's  apparent  diame- 
ter subtends  an  angle  of  32'  3".  The  true  diameter,  there- 
fore, must  be  882,000  miles.  But  the  diameter  of  the 
earth  is  short  of  8000  miles. 

Such,  therefore,  are  the  dimensions  of  the  orbit  of  the 
earth,  and  of  the  bodies  concerned  in  it.     We  are  now  in.  a 
position  to  verify  all  that  has  been  said  in  respect  of  the 
relations  of  these  bodies  ;  for,  calling  to  mind  what  was 
proved   in  Lecture  XXI,  respecting  bodies  situated    as 
these  are,  we  see  that  in  strictness  the  one  cannot  revolve 
round  the  other,  but  both  revolve  round  their  common  cen- 
ter of  gravity.     Recollecting  also  that  the  center  of  grav- 
ity of  two  bodies  is  at  a  distance  inversely  proportional 
to  their  weights,  and  that  the  sun  is  354,936  times  heavier 
than  the  earth,  it  follows  that  this  point  is  only  2C7  miles 
from  his  center.     So,  therefore,  with  scarce  an  error,  the 
center  of  the  sun  may  be  assumed  as  the  center  of  the 
earth's  orbit,  and  with  truth  she  may  be  spoken  of  as  re- 
volving around  him. 

Occupying  such  a  central  position,  this  enormous  globe 
is  discovered  to  rotate  on  an  axis  inclined  82°  40'  to  the 
plane  of  the  ecliptic,  making  one  rotation  in  twenty-five 
days  and  ten  hours,  in  a  direction  from  west  to  east.  This 
is  proved  by  spots  which  appear  from  time  to  time  on  his 
surface,  and  follow  his  movements.  He  is  the  great  source 
of  light  and  heat  to  us,  and  determines  the  order  of  the 
seasons.  His  weight  is  five  hundred  times  greater  than 
that  of  all  the  planets  arid  satellites  of  the  solar  system. 
though  he  is  not  of  greater  density  than  water. 

In  Fig.  344  we  have  a  general  representation  of  the 
appearance  of  the  solar  spots.  They  consist  of  a  dark 
nucleus,  surrounded  by  a  penumbra,  and  are  very  varia- 

What  is  the  distance  of  the  earth  from  the  sun  ?  What  is  the  actual 
diameter  of  the  sun  ?  At  what  distance  is  the  center  of  gravity  of  the  two 
bodies  from  the  sun's  center  ?  How  is  it  known  that  the  sun  rotates  on 
his  axis  ?  What  is  the  period  of  that  rotation  ?  Describe  the  phenomena 
of  his  spots. 


SPOTS    ON    THE    SUN. 


325 


ble,  both  in  number  and  size.  Sometimes  for  a  consider- 
able period  scarce  any  are  seen,  and  tben  they  occur  in 
great  numbers  in  irregular  clusters.  Their  size  varies 

Fig.  344. 


from  Jj  to  T£o-  part  of  the  sun's  diameter.  They  are, 
therefore,  of  enormous  dimensions,  often  greatly  exceed- 
ing the  surface  of  the  earth.  Their  duration  is  also  very 
variable.  Some  have  lasted  for  ten  weeks,  but  more  com- 
monly they  disappear  in  the  course  of  a  month  or  less. 
They  seem  to  be  the  seats  of  violent  action,  undergoing 
great  changes  of  form,  not  only  in  appearance,  but  also  in 
reality.  On  their  first  appearance  on  the  sun's  eastern 
edge,  they  move  slowly — they  move  rapidly  as  they  ap- 
proach the  middle  of  his  disc,  and  move  slowly  again  as 
they  pass  to  the  western  edge.  This  is,  however,  an  op- 
tical illusion,  due  to  the  globular  figure  of  the  sun.  They 
rarely  appear  at  a  greater  distance  than  from  30°  to  50° 
from  the  sun's  equator,  and  cross  his  disc  in  thirteen  days 
and  sixteen  hours.  Their  apparent  revolution  is,  there- 
fore, twenty-seven  days  and  eight  hours ;  and,  making  al- 
lowance for  the  simultaneous  movement  of  the  earth,  this 


326 


THE    SEASONS. 

gives  for  the  sun's  rotation  on  his  axis  twenty-five  days 
and  ten  hours. 

To  explain  the  occurrence  of  the  seasons — spring,  sum- 
mer, autumn,  and  winter — it  is  to  be  understood  that  the 
earth's  axis  of  rotation,  for  the  reasons  explained  in  Lec- 
ture XXI,  always  points  to  the  same  direction  in  space, 
and,  therefore,  as  the  earth  is  translated  round  the  sun,  is 
always  parallel  to  itself. 

Let,  therefore,  S,  Fig.  345,  be  the  sun,  and  E  E  E,  &c.t 
the  positions  the  earth  respectively  occupies  in  the  months 
marked  in  the  figure.  Her  position  is,  therefore,  in  Libra 
at  the  vernal  equinox,  in  Aries  the  autumnal,  in  Capricorn 
at  the  summer,  and  in  Cancer  at  the  winter  solstice.  lu 
these  different  positions,  P  m  represents  the  axis  of  the 
earth  always  parallel  to  itself,  as  has  been  said.  Now, 
from  the  globular  form  of  the  earth,  the  sun  can  only  shine 
on  one  half  at  a  time.  Let,  therefore,  the  shaded  portions 
represent  the  dark,  and  the  light  portions  the  illuminated 
halves.  Further,  in  all  the  different  positions,  let  E  G 
represent  the  ecliptic,  P  e  the  arctic  circle,  and  d  m  the 
antarctic. 

Now,  when  the  earth  is  in  the  position  marked  Aries, 
both  poles,  P  m,  fall  just  with  the  illuminated  half.  It  is, 
therefore,  day  over  half  the  northern  and  half  the  south- 
ern hemispheres  at  once.  And  as  the  earth  turns  round 
on  her  axis,  the  day  and  night  must  each  be  of  equal 
length — that  is  to  say,  twelve  hours  long — all  over  the 
globe.  Of  course,  precisely  the  same  holds  for  the  posi- 
tion at  Libra.  The  former  corresponds  to  September, 
the  latter  to  March. 

.  But  when  the  earth  reaches  Capricorn  in  June,  one  of 
her  poles,  P,  will  be  in  the  illuminated  half,  the  other,  m, 
in  the  dark  ;  and  for  a  space  reaching  from  P  to  e,  and  m 
to  d,  a  certain  portion  of  her  surface  will  also  be  illumin- 
ated, or  also  in  shadow.  The  illuminated  space,  P  e,  as 
the  earth  makes  her  daily  rotation,  will  be  exposed  to  the 
sun  all  the  time  ;  the  dark  space,  m  d,  will  be  all  the  time 
in  shadow.  At  this  period  of  the  year  the  sun  never  sets 
at  the  north  polar  circle,  and  never  rises  at  the  south. 
And  the  converse  of  all  this  happens  when  the  earth 
moves  round  to  Cancer,  in  December. 

Why  does  the  earth's  axis  always  point  in  the  same  direction  ?  Ex- 
plain the  phenomena  of  the  seasons. 


328  THE    SOLAR    SYSTEM. 

The  temperature  of  any  place  depends  on  the  amount 
of  heat  it  receives  from  the  sun.  During  the  day  the  earth 
is  continually  warming;  during  the  night  cooling.  When 
the  sun  is  more  than  twelve  hours  above  the  horizon,  and 
less  than  twelve  below,  the  temperature  rises,  and  con- 
versely. When  the  earth  moves  from  Libra  to  Capri- 
corn, in  the  northern  hemisphere,  the  days  grow  longer 
and  the  nights  shorter,  and  the  rise  of  temperature  we  call 
the  approach  of  spring.  As  she  passes  from  Capricorn 
to  Aries,  summer  comes  on.  From  Aries  to  Cancer,  the 
night  becomes  longer  than  the  day,  and  it  is  autumn — the 
reverse  taking  place  from  Cancer  to  Libra.  It  is  also  to 
be  remarked,  that  similar  but  reverse  phenomena  are  oc- 
curring for  the  southern  hemisphere.  This,  therefore,  ac- 
counts for  the  seasons,  and  accounts  for  all  their  attendant 
phenomena,  that  the  sun  never  sets  in  the  polar  circles 
during  summer,  nor  rises  during  winter. 


LECTURE  LXV. 

THE  SOLAR  SYSTEM. —  The  Planetary  Bodies. — Inferior 
and  Superior  Planets. — Mercury. —  Venus,  her  motions 
and  phases. —  Transits  of  Venus  over  the  Sun. —  Their 
importance. — Mars,  his  physical  appearance. 

HAVING  established  the  general  relations  of  the  earth 
and  sun,  and  shown  how  the  former  revolves  round  the 
latter  in  an  elliptic  orbit,  we  proceed,  in  the  next  place, 
to  a  description  of  the  solar  system, 

It  has  already  been  stated  that  among  the  stars  thei»e 
are  some  which  plainly  possess  proper  motions,  some- 
times being  found  in  one  part  of  the  heavens  and  some- 
times in  another.  To  these,  from  -their  wandering1  mo- 
tion, the  name  of  planets  has  been  given.  Like  the  earth, 
they  revolve  in  elliptic  orbits  round  the  sun.  Their  names, 
commencing  with  the  nearest  to  the  sun,  are — 

Mercury,  Juno,  Jupiter, 

Venus,  Ceres,  Saturn, 

Earth,  Pallas,  Uranus, 

Mars,  Astrea,  Neptune. 
Vesta, 

On  what  does  the  temperature  of  any  place  depend  ?  How  is  this  con- 
nected with  the  seasons ?  Wljat  are  the  planets?  Mention  their  names. 


MERCURY. 


329 


There  are,  therefore,  two  whose  orbits  are  included  in 
that  of  the  earth,  the  others  are  on  the  outside  of  it. 

MERCURY  always  appears  in  the  close  neighborhood  of 
the  sun,  and  hence  is  ordinarily  difficult  to  be  seen.  In 
the  evening,  after  sunset,  he  may,  at  the  proper  time,  be 
discovered,  but,  soon  retracing  his  path,  is  lost  among  the 
solar  rays.  After  a  time  he  reappears  in  the  morning, 
and  proceeding  farther  and  farther  from  the  sun,  with  a 
velocity  continually  decreasing,  he  finally  becomes  station- 
ary, and  then  returns,  to  reappear  again  in  the  evening. 

The  distance  of  this  planet  from  the  sun  is  more  than 
37,000,000  of  miles,  his  diameter  3200,  he  turns  on  his 
axis  in  24h.  5'  3'',  and  moves  in  his  orbit  with  a  velocity 
of  111,000  miles  in  an  hour. 

VENUS,  which  is  the  next  of  the  planets,  and,  like  Mer- 
cury, is  inferior — that  is,  has  her  orbit  interior  to  that  of 
the  earth — from  her  magnitude  and  position,  enables  us 
to  trace  the  phenomena  of  such  a  planet  in  a  clear  and 

Fig.  346. 


Under  what  circumstances  may  Mercury  be  seen?     What  is  his  dis- 
tance from  the  sun,  his  diameter,  and  the  time  of  his  rotation  ? 


330  VENUS. 

perfect  manner.  She,  too,  is  seen  alternately  as  an  even- 
ing and  morning  star,  being  first  discovered,  as  at  A,  Fig. 
346,  emerging  from  the  rays  of  the  sun,  and  moving  wilh 
considerable  rapidity  from  A  toward  B.  Let  K  be  the 
position  of  the  observer  on  the  earth,  which,  for  the  pres- 
ent, we  will  suppose  to  be  stationary.  To  such  an  ob- 
server the  motion  of  Venus,  as  she  recedes  from  the  sun, 
appears  to  become  slower  and  slower,  then  to  cease. 
And  now  the  planet,  passing  from  C  to  E,  appears  to 
have  a  retrograde  motion,  the  velocity  of  which  contin- 
ually increases,  then  again  lessens  as  she  moves  toward 
G,  then  ceases;  and,  lastly,  the  planet  moves  toward  A 
with  a  continually  accelerated  motion. 

All  this  is  evidently  the  effect  which  must  ensue  with  a 
body  pursuing  an  interior  orbit.  The  stationary  appear- 
ance arises  from  the  circumstance  that  at  one  point,  C, 
she  is  coming  toward  the  earth,  at  the  opposite,  Gr,  re- 
treating from  it;  while  at  A  and  at  E  she  is  crossing  the 
field  of  view. 

But  the  planets  shine  only  by  the  light  of  the  sun.  Ve- 
nus, moving  thus  in  an  interior  orbit,  ought,  therefore,  to 
exhibit  phases.  Thus,  in  Fig.  347,  when  she  first  emerges 
from  the  rays  of  the  sun  on  the  opposite  side,  as  respects 
the  earth',  a  position  which  is  called  her  superior  con- 
junction, A,  she  must  exhibit  to  us  the  whole  of  her  il- 
luminated disc  ;  but,  as  she  passes  from  A  to  B,  a  portion 
of  her  unilluminated  hemisphere  is  gradually  exposed  to 
view.  This  increases  at  D  ;  and  at  E  we  see  half  of  tho 
illuminated  and  half  of  the  dark  hemisphere.  She  looks, 
therefore,  like  a  little  half  moon.  As  she  comes  into  the 
position  F  Gr  H  we  see  more  and  more  of  her  dark  side. 
She  becomes  a  thinner  and  thinner  crescent,  and  at  I  is 
extinguished ;  and,  passing  from  this  toward  L  M  N  O, 
and  from  that  to  A,  we  gradually  recover  sight  of  more 
and  more  of  her  illuminated  disc. 

These  phenomena  must  necessarily  hold  for  a  planet 
moving  in  an  interior  orbit,  and  were  predicted  before 
the  invention  of  the  telescope.  That  instrument  estab- 
lished the  accuracy  of  the  prediction. 

The  points  E  and  O  are  the  points  of  greatest  elonga- 
tion, Ais  the  superior  conjunction,  and  I  the  inferior. 

What  phenomena  does  Venus  exhibit?  How  do  we  account  for  her 
direct  and  retrograde  motions  ?  Why  does  she  exhibit  phases  ? 


PHASES    OF    VENUS. 
Fif.  347. 


331 


Common  observation  shows  that  this  planet  differs  very 
much  at  different  times  in  brilliancy.  Two  causes  affect 
her  in  this  respect : — 1st,  the  different  amount  of  illumi- 
nated surface  which  we  perceive ;  2d,  the  difference  of 
apparent  magnitude  of  the  planet  as  she  changes  position 
in  her  orbit.  On  her  approach  toward  the  earth  from  E 
to  H  the  illuminated  portion  visible  lessens ;  but  then  her 
dimensions  increase  by  reason  of  her  proximity.  The 


What  are  the  points  of  her  greatest  elongation  and  the  superior  and  in- 
ferior conjunction  1    What  causes  affect  the  brilliancy  of  this  planet  ? 


332  TRANSITS    OF    VENUS. 

maximum  of  brilliancy  takes  place  when  she  is  about  40° 
from  the  sun. 

Moreover,  it  is  obvious  that  at  certain  intervals,  at  the 
tim^  of  the  inferior  conjunction,  both  this  and  the  preceding 
plS.net  must  appear  to  cross  the  face  of  the  sun.  To  this 
phenomenon  the  name  of  a  transit  is  given.  The  planet 
then  appears  as  a  round  black  spot  or  disc  projected  on  the 
sun.  In  the  case  of  Venus,  these  transits  take  place  at  in- 
tervals of  about  eight  and  one  hundred  and  thirteen  years. 
They  furnish  the  most  exact  means  of  determining  the 
sun's  parallax.  Let  A  B,  Fig.  348,  be  the  earth,  V  Ve- 

.  348. 


nus,  S  the  sutn.  Let  a  transit  of  the  planet  be  observ- 
ed by  two  spectators,  A  J>,  at  the  opposite  points  of 
that  diameter  of  the  earth,  perpendicular  to  the  ecliptic. 
Then  the  spectator  at  A  will  see  Venus  projected  on  the 
sun's  disc  at  C,  and  B  at  D  ;  but  the  angle  A  V  B  is 
equal  to  the  angle  C  V  D  ;  and  since  the  distance  of  the 
earth  from  the  sun  is  to  that  of  Venus  from  the  same 
body,  as  about  2|  to  1,  C  D  will  occupy  on  the  sun's  disc 
a  space  2£  times  that  under  which  the  earth's  diameter  is 
seen — that  is  to  say,  five  times  as  much  as  the  horizontal 
parallax.  The  sun's  parallax,  as  determined  from  the 
transit  of  1769,  is  8"-6  nearly. 

The  period  occupied  by  this  planet  in  performing  her 
revolution  round  the  sun  is  224*  days,  16  hours,  42  min- 
utes, 25.5  seconds.  The  orbit  is  inclined  to  the  ecliptic 
3°  23'  25".  She  revolves  on  her  axis  in  23h  21'  19". 
Her  diameter  is  about  7800  miles.  She  is,  therefore, 
very  nearly  the  size  of  the  earth. 

When  is  she  most  brilliant?  What  is  a  transit?.  At  what  intervals 
do  these  take  place  in  the  case  of  Venus?  How  are  these  used  to 
determine  parallax  ?  What  is  the  period  of  revolution  of  this  planet  ? 
What  is  her  diameter? 


MARS.  333, 

MARS  is  the  next  planet,  the  earth  intervening  between 
him  and  Venus,  his  orbit  is,  therefore,  an  exterior  one, 
and  in  common  with  the  others  that  follow,  he  is  desig- 
nated as  a  superior  planet.  He  is  of  a  reddish  color,  and 
sometimes  appears  gibbous,  and  both  when  in  conjunction 
and  opposition  exhibits  a  full  disc.  The  diameter  differs 
very  greatly  according  to  his  position,  and  with  it,  of 
course,  his  brilliancy  varies.  The  distance  from  the  sun 
is  about  146  millions  of  miles,  he  revolves  on  his  axis  in 
24h  31'  32",  the  inclination  of  his  orbit  to  the  ecliptic  is 
1°:.£F  I".  As  with  the  earth  his  polar  diameter  is  shorter 
than  his  equatorial. 

The  physical  appearance  of  Mars  is  somewhat  remark- 
able. His  polar  regions,  when  seen  through  a  telescope, 
have  a  brilliancy  so  much  greater  than  the  rest  of  his  disc 
that  there  can  be  little  doubt  that,  as  with  the  earth  so 
with  this  planet,  accumulations  of  ice  or  snow  take  place 
during  the  winters  of  those  regions.  In  1781  the  south 
polar  spot  was  extremely  bright ;  for  a  year  it  had  not 
been  exposed  to  the  solar  rays.  The  color  of  the  planet 
most  probably  arises  from  a  dense  atmosphere  which 
surrounds  him,  of  the  existence  of  which  there  is  other 
proof  depending  on  the  appearance  of  stars  as  they  ap- 
proach him ;  they  grow  dim  and  are  sometimes  wholly 
extinguished  as  their  rays  pass  through  that  medium. 

Fig.  349. 


Fig.  349  represents  the  telescopic  appearance  of  Mars, 
according  to  Herschel ;  a  is  the  polar  spot. 

Why  is  Mars  called  a  superior  planet  ?  Does  he  exhibit  phases  ?  What 
is  there  remarkable  respecting  his  physical  appearance  ?  What  reasons 
are  there  fur  supposing  he  has  a  dense  atmosphere? 


334 


THE    ASTEROIDS. 


LECTURE  LXVI. 

THE  SOLAR  SYSTEM. —  The  Five  Asteroids. — Jupiter  and 
his  Satellites.  —  Saturn,  his  Rings  and  Satellites.  — 
Uranus. — Neptune. —  The  Comets. — Returns  of  Halley's 
Comet. — Comets  of  Enckc  and  Biela. 

OUTSIDE  of  the  orbit  of  Mars  there  occur  five  telescopic 
planets  closely  grouped  together — they  are  VESTA.  JUNO, 
CERES,  PALLAS,  and  ASTREA.  They  have  all  been  dis- 
covered within  the  present  century,  the  last  of  them  in 
1846.  From  their  smallness  and  distance  they  are  far 
from  being  well  known.  The  following  table  contains 
the  chief  facts  in  relation  to  them. 


Period  of  Revolu- 
tion. 

Inclination  of 
Orbit  to  Ecliptic. 

Distance  in 
miles. 

Diameter 
in  miles. 

Vesta 
Juno 
Ceres 
Pallas 
Astrea 

3    yrs.  66d.    4  h. 
4   yrs.!28d. 
4£  yrs. 
4   yrs.  7  m.  11  d. 
4    yrs.  2m.    4  d. 

7°    8' 
13°    4Y 
](P  37'  25" 
34°  37'  30" 
5°  2<y 

225.000.000 
256.000.000 
264.000.000 
267.000.000 
250  000  000 

1320 
1320 
1920 

It  has  been  thought  that  these  small  planets  are  merely 
the  fragments  of  a  much  larger  one  which  has  been  burst 
asunder  by  some  catastrophe.  There  seems  to  be  some 
foundation  for  this  opinion.  It  has  been  asserted  that 
they  are  not  round,  but  present  angular  faces.  They  are 
also  enveloped  in  dense  atmospheres,  and  in  the  case  of 
Juno  and  Pallas,  their  orbits  are  greatly  inclined  to  the 
ecliptic.  These  planets  are  sometimes  called  asteroids. 

JUPITER,  the  largest  and  perhaps  the  most  interesting 
of  the  planets,  has  his  orbit  immediately  beyond  that  of 
the  asteroids.  He  always  presents  his  full  disc  to  the 
earth,  and  performs  his  revolution  round  the  sun  in  11 
years  318  days,  at  a  distance  of  495  millions  of  miles. 
He  is  nearly  1500  times  the  size  of  the  earth,  being 
89,000  miles  in  diameter. 


What  planets  come  next  in  order  to  Mars  '(  What  is  there  remarkable 
respecting  the  size  and  orbits  of  these  planets?  Under  what  name  do 
they  also  go  ?  What  is  the  position  and  size  of  Jupiter  ? 


JUPITER.  335 

Immediately  after  the  invention  of  the  telescope,  it  was 
discovered  by  Galileo  that  Jupiter  is  attended  by  four 
satellites  or  moons,  which  revolve  round  him  in  orbits 
almost  in  the  plane  of  his  equator.  Each  of  these  satel- 
lites revolves  on  its  own  axis  in  the  same  time  that  it 
goes  round  its  primary,  so  that,  like  our  own  moon,  they 
always  turn  the  same  face  to  the  planet.  Like  our 
moon,  also,  they  exhibit  the  phenomena  of  lunar  and 
solar  eclipses.  Advantage  has  been  taken  of  these 

Fig.  350. 


eclipses  to  determine  terrestrial  longitudes,  and  we  have 
already  seen  it  was  from  them  that  the  progressive  mo- 
tion of  light  was  first  established. 

Juph^r  revolves  on  his  axis  in  9h.  56'.  This  rapid  ro- 
tation, therefore,  causes  him  to  assume  a  flattened  form — 
his  polar  axis  being  -fa  shorter  than  his  equatorial,  and  as 
his  axis  is  nearly  perpendicular  to  the  plane  of  his  orbit, 
his  days  and  nights  must  be  equal,  and  there  can  be  but 
little  variation  in  his  seasons.  His  disc  is  crossed  by  belts 
or  zones,  which  are  variable  in  number  and  parallel  to  his 
equator. 

SATURN,  which  is  the  next  planet,  performs  his  revolu- 
tion round  the  sun  in  about  twenty-nine  years  and  a  half, 
at  a  distance  of  915  millions  of  miles.  The  inclination  of 
his  orbit  to  the  ecliptic  is  2°  30'.  He  is  about  900  times 
larger  than  the  earth,  being  79,000  miles  in  diameter. 

How  many  satellites  has  he  ?  What  advantage  has  been  taken  of  their 
eclipses  ?  What  is  the  time  of  rotation  of  this  planet  on  his  axis  ?  What 
is  the  relation  of  his  equatorial  to  his  polar  diameter?  What  is  the  dis- 
tance and  size  of  Saturn  ? 


336  SATURN    AND    URANUS. 

He  turns  on  his  axis  in  10£  hours,  and  the  flattening  of 
his  polar  diameter  is  y^. 

Seen  through  the  telescope,  Saturn  presents  a  most  ex- 
traordinary aspect.  His  disc  is  crossed  with  belts,  like 
those  of  Jupiter;  a  broad  thin  ring,  or  rather  combina- 
tion of  rings,  surrounds  him,  and  beyond  this  seven  satel- 
lites revolve.  The  ring  is  plainly  divided  into  two  con- 
centric portions,  a  b,  as  seen  in  Fig.  351,  and  other  sub- 

Fig.  351. 


divisions  have  been  suspected.  The  larger  ring  is  nearly 
205,000  miles  in  exterior  diameter,  and  the  space  between 
the  two  2680  miles.  The  rings  revolve  on  their  own  cen- 
ter— which  does  not  exactly  coincide  with  the  center  of 
Saturn — in  about  10  hours  and  20  minutes.  The  excen- 
tricity  of  the  rings  is  essential  to  their  stability. 

URANUS,  discovered  in  1781,  by  Herschel,  revolves  in 
an  orbit  exterior  to  Saturn,  in  a  period  of  about  84  years, 
and  at  a  distance  of  1840  millions  of  miles.  The  incli- 
nation of  its  orbit  to  the  ecliptic  is  46^'.  It  can  only  be 
seen  by  the  telescope.  Its  diameter  is  35,000  miles.  Six 
satellites  have  been  discovered. 

By  what  extraordinary  appendage  is  he  attended?  How  many  satellites 
has  he  ?  What  is  the  distance  of  Uranus  ?  By  whom  was  he  discovered  T 


NEPTUNE.  337 

NEPTUNE. — This  planet  was  discovered  in  1846,  in  con- 
sequence of  mathematical  investigations  made  by  Adams 
and  Leverrier,  with  a  view  of  explaining  the  perturba- 
tions of  Uranus.  It  was  also  seen  in  1795  by  Lalande, 
and  regarded  by  him  as  a  fixed  star.  Its  period  is  about 
166  years — very  nearly  double  that  of  Uranus.  The  in- 
clination of  its  orbit  is  1°  45'.  The  excentricity  is  only 
0.005.  The  orbit  is,  therefore*  more  nearly  a  perfect 
circle  than  that  of  any  other  planet.  There  is  reason  to 
believe  that  Neptune  is  surrounded  by  a  ring  analogous 
to  the  ring  of  Saturn. 

The  planetary  bodies  now  described,  with  their  attend- 
ant satellites  and  the  sun,  taken  collectively,  constitute 
the  solar  system,  a  representation  of  which,  as  respects 
the  order  in  which  the  bodies  revolve,  is  given  in  Fig. 
352.  In  the  center  is  the  sun,  and  in  close  proximity  to 

Fig.  352. 


him  revolves  Mercury,  outside  of  whose  orbit  comes  Ve- 
nus.    Then  follows  the  earth,  attended  by  her  satellite, 

What  is  the  position  of  Neptune  ?    Of  what  is  the  solar  system  com- 
posed ? 

P 


338  COMETS. 

the  moon.  Beyond  the  earth's  orbit  comes  Mars  ;  then 
come  the  asteroids,  followed  by  Jupiter,  with  his  four 
moons.  Still  more  distant  is  Saturn,  surrounded  by  his 
rings  and  seven  satellites ;  then  Uranus,  with  six  ;  and 
lastly,  so  far  as  our  present  knowledge  extends,  comes  the 
recently-discovered  planet  Neptune. 

Such  a  representation  as  that  given  in  Fig.  352,  can 
merely  illustrate  the  ortftr  in  which  the  members  of  the 
solar  system  occur,  but  can  afford  no  suitable  idea  of  their 
relative  magnitudes  aud  distances.  Thus,  in  that  figure, 
the  apparent  diameter  of  the  sun  is  about  the  tenth  of  an 
inch,  and  were  the  proportions  maintained,  the  diameter 
of  the  orbit  of  the  planet  Neptune  should  be  about  fifty 
feet.  A  similar  observation  might  be  made  as  respects 
the  planetary  masses. 

But  besides  these  bodies,  there  are  others  now  to  be 
described,  which  are  members  of  our  solar  system.  They 
are  the  comets.  They  move  in  very  excentric  orbits,  and 
are  only  visible  to  us  when  near  their  perihelion.  In  ap- 
pearance they  differ  very  greatly  from  one  another,  but 

Fig.  353. 


most  commonly  consist  of  a  small  brilliant  point,  from 
which  there  extends  what  is  designated  the  tail.     Some- 

In  what  respects  are  such  representations  of  the  solar  system  as  that  in 
Fig.  352  imperfect  ?  What  are  comets  ?  What  is  remarkable  as  respects 
their  physical  constitution  ? 


RETURN     OF    COMETS.  339 

times  they  are  seen  without  this  remarkable  appendage. 
In  other  instances  it  is  of  the  most  extraordinary  length, 
and  in  former  ages,  when  the  nature  of  these  bodies  was 
ill  understood,  occasioned  the  utmost  terror,  for  comets 
were  looked  upon  as  omens  of  pestilence  and  disaster. 
The  comet  of  1811  had  a  tail  nearly  95  millions  of  miles 
in  length — that  of  1744  had  several,  spreading  forth  in 
the  form  of  a  fan. 

The  history  of  the  discovery  of  the  nature  of  comets  is 
very  interesting.  Dr.  Halley,  a  friend  of  Sir  I.  Newton, 
had  his  attention  first  fixed  on  the  probability  that  several 
bodies,  recorded  as  distinct,  might  be  the  periodic  returns 
of  the  same  identical  comet,  and  closely  examining  one 
which  was  seen  in  1682,  came  to  the  conclusion  that  it 
regularly  appeared  at  intervals  of  seventy-five  or  seventy- 
six  years.  He  therefore  predicted  that  it  ought  to  reap- 
pear about  the  beginning  of  the  year  1759.  The  comet 
actually  came  to  its  perihelion  on  March  the  13th  of  that 
year,  and  again,  after  an  interval  of  seventy-six  years,  in 
1835. 

Besides  the  comet  of  Halley,  there  are  two  others,  the 
periodic  returns  of  which  have  been  repeatedly  observed. 
These  are  the  comet  of  Encke  and  that  of  Biela.  The 
former  is  a  small  body  which  revolves  in  an  elliptical  or- 
bit, with  an  inclination  of  13£°  in  about  1200  days.  Its 
nearest  approach  to  the  sun  is  about  to  the  distance  of  the 
planet  Mercury;  its  greatest  departure  somewhat  less 
than  the  distance  of  Jupiter.  Its  motion  is  in  the  same 
direction  as  that  of  the  planets. 

The  comet  of  Biela  has  a  period  of  2460  days.  It  moves 
in  an  elliptical  orbit,  the  length  of  which  is  to  the  breadth 
as  about  three  to  two.  Its  nearest  approach  to  the  sun  is 
about  equal  to  the  distance  of  the  earth ;  its  greatest  re- 
moval somewhat  beyond  that  of  Jupiter.  It  reappears 
with  great  regularity,  but  in  the  month  of  January,  1846,  it 
exhibited  the  wonderful  phenomenon  of  a  sudden  division, 
two  comets  springing  out  of  one.  This  fact  was  first  seen 
by  Lieutenant  Maury,  at  the  National  Observatory  at 
Washington. 

Nothing  is  known  with  precision  respecting  the  nature 

When  was  the  periodic  return  of  comets  first  detected  ?  What  other 
two  comets  have  been  frequently  re-observed  ?  What  remarkable  result 
lias  been  noticed  respecting  Biela's  comet  ? 


340  THE  SECONDARY  PLANETS. 

of  these  bodies.  They  are  apparently  only  attenuated 
masses  of  gas,  for  it  is  said  that  through  them  stars  of  the 
sixth  or  seventh  magnitude  have  been  seen.  In  the  case 
of  some  there  appears  to  have  been  a  solid  nucleus  of 
small  dimensions. 


LECTURE  LXVII. 

THE  SECONDARY  PLANETS  OR  SATELLITES. —  The  Moon, 
her  Phases,  her  Period  of  Revolution,  her  Physical  ap- 
pearance— always  presents  the  same  face. — Eclipses  of  the 
Moon. — Eclipses  of  the  Sun. — Recurrence  of  Eclipses. — 
Occultations. 

THE  motions  of  the  secondary  bodies  of  the  solar  sys- 
tem, the  satellites,  and  more  especially  the  phenomena 
of  our  own  moon,  deserve,  from  their  importance,  a  more 
detailed  investigation.  To  these,  therefore,  I  proceed  in 
this  lecture. 

That  the  moon  has  a  proper  motion  in  the  heavens  the 
observations  of  a  single  night  completely  proves.  She 
is  translated  from  west  to  east,  so  that  she  comes  to  the 
meridian  about  forty-five  minutes  later  each  day,  and 
performs  her  revolution  round  the  earth  in  about  thirty 
days,  exhibiting  to  us  each  night  appearances  that  are 
continually  changing,  and  known  under  the  name  of 
phases. 

First  when  seen  in  the  west,  in  the  evening,  she  is  a 
crescent,  the  convexity  of  which  is  turned  to  the  sun. 
From  night  to  night  the  illuminated  portion  increases, 
and  about  the  seventh  day  she  is  half-moon.  At  this  time 
she  is  said  to  be  in  her  quadrature  or  dichotomy.  The 
enlightened  portion  still  increasing,  she  becomes  gibbous, 
and  about  the  fifteenth  day  is  full.  She  now  rises  at  sun- 
set. 

From  this  period  she  continually  declines,  becomes  gib- 
bous, and  at  the  end  of  a  week  half-moon.  Still  further 
she  is  crescentic ;  and  at  last,  after  twenty-nine  or  thirty 
days,  disappears  in  the  rays  of  the  sun. 

What  is  supposed  to  be  the  physical  constitution  of  these  bodies  ?  What 
is  the  direction  of  the  moon's  motion  ?  In  what  time  is  a  complete  revo- 
lution completed  ?  What  are  her  phases  ?  Describe  their  order. 


PHASES    OP    THE    MOON.  341 

At  new-moon,  she  is  said  to  be  in  conjunction  with  the 
sun,  at  full-moon  in  opposition ;  and  these  positions  are 
called  syzygies;  the  intermediate  points  between  the 
svzygies  an<i  quadratures  are  octants. 


Fiff.354. 


The  cause  of  the  moon's  phases  admits  of  a  ready  ex- 
planation on  the  principle  that  she  is  a  dark  body,  re- 
flecting the  light  of  the  sun,  and  moving  in  an  orbit  round 
the  earth.  Thus,  let  S,  Fig.  364,  be  the  sun,  E  the  earth, 
and  a  b  c,  &c.,  the  moon  seen  in  different  positions  of  her 
orbit.  From  her  globular  figure,  the  rays  of  the  sun  can 
only  illuminate  one  half  of  her  at  a  time,  and  necessarily 
that  half  which  looks  toward  him.  Commencing,  there- 
fore, at  the  position  a,  where  both  these  bodies  are  on 
the  same  side  of  the  earth,  or  in  conjunction,  the  dark 
side  of  the  moon  is  turned  toward  us,  and  she  is  invisi- 
ble ;  but  as  she  passes  to  the  position  £,  which  is  the  oc- 
tant, the  illuminated  portion  comes  into  view.  And  when 
she  has  reached  the  position  c,  her  quadrature,  we  see 
half  the  shining  and  half  the  dark  hemisphere.  Here, 
therefore,  she  is  half-moon.  From  this  point  she  now 
becomes  gibbous ;  and  at  e,  being  in  opposition,  exposes 
her  illuminated  hemisphere  to  us,  and  is,  therefore,  full- 
mcon.  From  this  point,  as  she  returns  through  f  g  kt 
she  runs  through  the  reverse  changes,  being  in  succes- 
sion gibbous,  half-moon,  crescentic,  and  finally  disappear- 
ing.  

What  are  the  syzygies,  and  quadratures,  and  octants  ?    What  is  the  ex- 
planation of  the  phases  ? 


342  .  THE    MOON. 

Viewed  through  a  telescope,  the  surface  of  the  moon 
is  very  irregular,  there  being  high  mountains  and  deep 
pits  upon  it.  These,  in  the  various  positions  she  assumes 
as  respects  the  sun,  cast  their  shadows,  which  are  the 
dark  marks  we  can  discover  by  the  eye,  on  her  disc,  and 
•which  are  popularly  supposed  to  be  water. 

Fig.  355. 


The  moon's  diameter,  measured  at  different  times,  va- 
ries considerably.  This,  therefore,  proves  that  she  is  not 
always  at  the  same  distance  from  the  earth  ;  and,  in  fact, 
she  moves  in  an  ellipsis,  the  earth  being  in  one  of  the 
foci.  Her  distance  is  about  230,000  miles.  She  accom- 
panies the  earth  round  the  sun,  and  turns  on  her  axis  in 
precisely  the  same  length  of  time  which  it  takes  her  to 
perform  her  monthly  revolution.  Consequently,  she  al- 
ways presents  to  us  the  same  face.  Her  orbit  is  inclined 
to  that  of  the  ecliptic,  at  an  angle  of  little  more  than  five 

What  is  the  appearance  of  the  moon  seen  through  a  telescope  T  Is 
her  apparent  diameter  always  the  same  ?  What  is  her  distance  ?  What 
is  her  period  of  rotation  on  her  axis  ?  Does  she  always  present  exactly 
the  same  face  to  the  earth  ? 


ECLIPSE    OF    THE    MOON.  843 

degrees.  Its  points  of  intersection  with  the  ecliptic  are 
the  nodes.  Her  greatest  apparent  diameter  is  33£  min- 
utes. The  nodes  move  slowly  round  the  ecliptic,  in  a  di- 
rection contrary  to  that  of  the  sun,  completing  an  entire 
revolution  in  about  eighteen  years  and  a  half.  Although, 
for  the  most  part,  she  presents  the  same  face  to  the  earth, 
as  has  been  said,  yet  this,  in  a  small  degree,  is  departed 
from  in  consequence  of  her  libration.  This  takes  place 
both  in  longitude  and  latitude,  and  brings  small  portions 
of  her  surface,  otherwise  unseen,  into  view. 

The  relations  of  the  sun,  the  earth,  and  the  moon  to 
one  another  afford  an  explanation  of  the  interesting  phe- 
nomenon of  eclipses.  These  are  of  two  kinds — eclipses 
of  the  moon  and  those  of  the  sun. 

The  earth  and  moon  being  dark  bodies,  which  only 
shine  by  reflecting  the  light  of  the  sun,  project  shadows 
into  space.  Let,  therefore,  A  B,  Fig.  356,  be  the  sun, 
C  D  the  earth,  and  M  the  moon,  in  such  a  position,  as 
respects  each  other,  that  the  moon,  on  arriving  in  oppo- 
sition, passes  through  the  shadow  of  the  earth.  The  light 
is,  therefore,  cut  off,  and  a  lunar  eclipse  takes  place. 

Fig.  356. 


The  shadow  cast  by  the  earth  is  of  a  conical  foi^i,  a 
figure  necessarily  arising  from  the  great  size  of  the  sun 
when  compared  with  that  of  the  earth.  The  semi-diame- 
ter of  the  shadow  at  the  points  where  the  moon  may 
cross  it  varies  from  about  37'  to  46' — that  is,  it  may  be 
as  much  as  three  times  the  semidiameter  of  the  moon. 
A  lunar  eclipse  may,  therefore,  last  about  two  hours. 

The  time  of  the  occurrence  of  an  eclipse  of  the  moon 
is  the  same  at  all  places  at  which  it  is  visible.  It  is,  of 
course  visible  at  all  places  where  the  moon  is  then  to  be 

How  many  kinds  of  eclipses  are  there  ?  Under  what  circumstance  does 
a  lunar  eclipse  take  place  ?  How  long  may  a  lunar  eclipse  last  ?  How  is 
its  magnitude  estimated  ? 


344  ECLIPSE    OF    THE    SUN. 

seen.  The  magnitude  of  the  eclipse  is  estimated  in  digits, 
the  diameter  of  the  moon  being  supposed  to  be  divided 
into  twelve  digits. 

Whatever  may  be  the  circumstances  under  which  a 
lunar  eclipse  takes  place,  the  shadow  of  the  earth  is  al- 
ways circular.  Advantage  has  already  been  taken  of  this 
fact  in  giving  proof  of  the  spherical  figure  of  the  earth. 

If  the  plane  of  the  moon's  orbit  were  not  inclined  to 
the  ecliptic  there  would  be  a  lunar  eclipse  every  full 
moon.  It  is  necessary,  therefore,  for  this  to  occur,  that 
the  moon  should  be  either  in  or  near  to  the  node,  so  that 
the  sun,  the  earth,  and  the  moon  may  be  in  the  same  line. 
It  was  explained  in  Lecture  XXXV.,  that  a  body  situated 
under  the  same  circumstances  as  those  under  which  the 
earth  is  now  considered  forms  a  penumbra  as  well  as  a 
true  shadow.  There  is,  therefore  a  gradual  obscuration 
of  light  as  the  moon  approaches  the  conical  shadow,  aris- 
ing from  its  gradual  passage  through  the  penumbra. 

An  eclipse  of  the  sun  takes  place  under  the  following 
circumstances.  Let  A  B,  Fig.  357,  be  the  sun,  M  the 
moon,  and  C  D  the  earth.  Whenever  the  moon  passes 

Kg.  357. 


B 

directly  between  the  earth  and  the  sun,  she  hides  his  disc 
from  us,  and  a  solar  eclipse  takes  place.  It  is  partial 
when  only  a  portion  of  the  sun  is  obscured,  annular  when 
a  ring  of  light  surrounds  the  moon  at  the  middle  of  the 
eclipse,  and  total  when  the  whole  sun  is  covered. 

As  the  moon  is  so  much  smaller  than  the  earth,  the 
conical  shadow  which  she  casts  can  only  cover  a  portion 
of  the  earth  at  a  time.  Solar  eclipses  occur  at  different 
times  to  different  observers,  and  in  this  respect,  therefore, 
eclipses  of  the  moon  are  more  frequently  observed  than 

What  is  to  be  observed  respecting  the  figure  of  the  earth's  shadow  ? 
Why  is  there  not  a  lunar  eclipse  every  month  ?  Under  what  circum- 
stance does  an  eclipse  of  the  sun  take  place?  Why  is  there  a  difference 
between  solar  and  lunar  eclipses  as  respects  the  time  at  which  they  are 
seen,  and  also  as  respects  their  relative  frequency  ? 


ECLIPSES.  345 

those  of  the  sun.  Like  lunar  eclipses,  solar  ones  can 
only  occur  in  or  near  one  of  the  nodes.  Solar  eclipses 
can  only  occur  at  new  moon,  and  lunar  at  full  moon. 

Like  the  earth,  the  moon  casts  a  penumbra ;  it  is  a  cone, 
the  axis  of  which  is  aline  joining  the  centers  of  the  moon 
and  sun,  and  the  vertex  of  which  is  a  point  where  the 
tangents  to  the  opposite  sides  of  the  bodies  intersect. 

Eclipses  recur  again  after  a  period  of  about  1S£  years. 
In  each  year  there  cannot  be  less  than  two  nor  more  than 
seven  eclipses  ^  in  the  former  case  they  are  both  solar,  in 
the  latter  there  must  be  five  of  the  sun  and  two  of  the 
moon.  There  must,  therefore,  be  at  least  two  eclipses 
of  the  sun  each  year,  and  cannot  be  more  than  three  of 
the  moon. 

The  satellites  which  move  round  Jupiter,  Saturn,  and 
Uranus,  exhibit  the  same  phenomena  of  phases  and 
eclipses  to  the  inhabitants  of  those  bodies  as  are  exhibited 
to  us  by  our  moon.  Advantage  has  been  taken  of  the 
eclipses  of  Jupiter's  satellites  for  the  purpose  of  deter- 
mining longitudes  upon  the  earth,  and  from  them  the 
progressive  motion  of  light  was  first  established. 

An  occupation  is  the  intervention  of  the  moon  between 
the  observer  and  a  fixed  star.  Occultations  may  be  used 
for  the  determination  of  longitudes. 

After  what  period  do  eclipses  recur  ?  How  may  they  occur  as  to  num- 
ber each  year?  What  use  is  made  of  the  eclipses  of  Jupiter's  satellites  ? 
What  is  an  occultation  ? 


346  THE    FIXED    STARS. 


LECTURE  LXVIII. 

THE  FIXED  STARS. — Apparent  Magnitudes. —  Constella- 
tions.—  The  Zodiac.  —  Nomenclature  of  the  Stars. — 
Double  Stars.  —  Parallax. — Distance  of  the  Stars. — 
Groups  of  Stars. — Nebula. —  Constitution  of  the  Uni- 
verse.— Nebular  Hypothesis. 

AV^iTH  the  exception  of  the  sun  and  moon,  the  heavenly 
bodies  hitherto  described  form  but  an  insignificant  por- 
tion of  the  display  which  the  skies  present  to  us.  For, 
besides  them  there  are  numberless  other  bodies  of  va- 
rious sizes  which,  for  very  great  periods  of  time,  maintain 
stationary  positions,  and  for  this  reason  are  designated  as 
fixed  stars. 

The  fixed  stars  are  classed  according  to  their  apparent 
dimensions  ;  those  of  the  first  magnitude  are  the  largest, 
and  the  others  follow  in  succession  ;  the  number  increases 
very  greatly  as  the  magnitudes  are  less.  Of  stars  of  the 
first  magnitude  there  are  about  eighteen,  of  those  of  th< 
second  sixty,  and  the  telescope  brings  into  view  tens  o 
thousands  otherwise  wholly  invisible  to  the  human  eye. 

From  very  early  times,  with  a  view  of  the  more  ready 
designation  of  the  stars,  they  have  been  divided  into  con- 
stellations ;  that  is,  grouped  together  under  some  imag- 
inary form.  The  number  of  these  for  both  hemispheres 
exceeds  one  hundred.  They  are  commonly  depicted  upon 
celestial  globes. 

The  ecliptic  passes  through  twelve  of  the  constella- 
tions, occupying  a  zone  of  sixteen  degrees  in  breadth, 
through  the  middle  of  which  the  line  passes.  This  zone 
is  called  the  zodiac,  and  its  constellations  with  their  signs 
are  as  follows : 

Aries      °P  Libra 

Taurus   b  Scorpio          ut 

Gemini  n  Sagittarius     $ 

Cancer  22  Capricornus  V? 

Leo        £1  Aquarius       ~ 

Virgo     n  Pisces  X 

What  are  the  fixed  stars  ?  How  are  they  divided  ?  How  many  of  the 
first  and  second  magnitudes  are  there  ?  What  are  constellations  ?  What 
is  the  zodiac  ?  Mention  the  constellations  of  it. 


DOUBLE    STARS.  347 

The  order  in  which  they  are  here  set  down  is  the 
order  which  they  occupy  in  the  heavens,  commencing 
with  the  west  and  going  east.  Motions  of  the  sun  and 
planets  in  that  direction  are,  therefore,  said  to  be  direct, 
and  in  the  opposite  retrograde. 

To  many  of  the  larger  stars  proper  names  have  been 
given.  These,  in  many  instances,  are  oriental,  such  as 
Aldebaran,  but  they  are  chiefly  designated  by  the  aid  of 
the  Greek  letters,  the  largest  star  in  any  constellation 
being  called  a,  the  second  (3,  &c.,  to  these  letters  the 
name  of  the  constellation  is  annexed. 

The  position  of  any  star  is  determined  by  its  declina- 
tion and  right  ascension,  and  though  these  positions  are 
commonly  regarded  as  fixed,  yet  the  great  perfection  to 
which  modern  astronomy  has  arrived  has  shown  that  the 
stars  are  affected  by  a  variety  of  small  motions,  although, 
in  some  instances,  these  may  arise  in  extrinsic  causes, 
such,  for  example,  as  in  the  case  of  aberration,  yet  there 
can  now  be  no  doubt  that  the  stars  have  proper  motions 
of  their  own.  This  is  most  satisfactorily  seen  in  the  case 
of  double  stars,  of  which  there  are  several  thousands. 
These  are  bodies  commonly  arranged  in  pairs  close  to- 
gether, the  physical  connection  between  them  is  established 
by  the  circumstance  that  they  revolve  round  one  another  ; 
thus,  y,  Virginis,  has  a  period  of  629  years,  and  e,  Bootis, 
one  of  1600  years. 

From  the  planets  the  stars  differ  in  a  most  striking 
particular  :  they  shine  by  their  own  light.  It  this  respect 
they  resemble  our  sun,  who  must  himself,  at  a  suitable 
distance,  exhibit  all  the  aspect  of  a  fixed  star.  We  there- 
fore infer  that  the  stars  are  suns  like  our  own,  each, 
probably  like  ours,  surrounded  by  its  attendant  but  in- 
visible planets  ;  and,  therefore,  though  the  number  of  the 
stars  as  seen  by  telescopes  may  be  countless,  the  number 
of  heavenly  bodies  actually  existing,  but  not  apparent 
because  they  do  not  shine  by  their  own  light,  must  be 
vastly  greater.  In  our  solar  system  there  are  between 
thirty  and  forty  opaque  globes  to  one  central  sun. 

It  is  immaterial  from  what  part  of  the  earth  the  fixed 

What  are  direct  and  what  retrograde  motions  ?  How  are  stars  designa- 
ted ?  How  is  their  position  determined  ?  How  is  it  known  that  some  of 
them  have  proper  motions  ?  What  are  double  stars  ?  In  what  respect  do 
stars  differ  from  planets  ? 


348  DISTANCE    OF    THE    STARS. 

stars  are  seen ;  they  exhibit  no  change  of  position,  and 
have  no  horizontal  parallax  :  an  object  8000  miles  in  di- 
ameter, at  that  distance  is  wholly  invisible  from  them. 
But  more,  when  viewed  at  intervals  of  six  months,  when 
the  earth  is  on  opposite  sides  of  her  orbit — a  distance  of 
190  millions  of  miles  intervening — the  same  result  holds 
good.  To  the  nearest  of  them,  therefore,  our  sun  must 
appear  as  a  mere  mathematical  lucid  point — that  is  to 
say,  a  star. 

In  Lecture  LXV.,  the  method  of  determining  the  dis- 
tance of  the  sun  has  been  given.  The  same  principles 
apply  in  the  determination  of  the  distance  of  a  fixed  star. 
The  horizontal  parallax  may  be  found  without  difficulty 
for  the  bodies  of  our  solar  system  :  it  is,  in  reality,  the  angle 
under  which  the  earth's  semi-diameter  is  seen  from  them. 
But  when  this  method  is  applied  to  the  fixed  stars,  it  is 
discovered  that  they  have  no  such  sensible  parallax;  and, 
therefore,  that  the  earth  is,  as  has  been  observed,  wholly  in- 
visible from  them.  This  is  illustrated  in  Fig.  358,  in  which 
let  S  be  the  sun,  A  B  C  D  the  earth,  moving  in  her  orbit, 
and  the  lines  A  «,  B  b,  C  c,  D  d  the  axis  of  the  earth, 
continued  to  the  starry  heavens.  This  axis,  we  have  seen 
in  Lecture  XXL,  is  always  parallel  to  itself;  it  would 
therefore  trace  in  the  starry  heavens  a  circle,  abed,  of 
equal  magnitude  with  the  earth's  orbit,  ABC  D — that  is, 
190  millions  of  miles  in  diameter.  If  H  be  a  star,  when 
the  earth  is  at  the  point  A  of  her  orbit  the  star  will  be 
distant  from  the  pole  of  the  heavens  by  the  distance  a  H, 
and  when  she  is  at  the  point  C,  by  the  distance  c  II.  It 
takes  the  earth  six  months  to  pass  from  A  to  C,  ]90  mil- 
lions of  miles.  But  the  most  delicate  means  have  hith- 
erto failed  to  detect  any  displacement  of  a  star,  such  as 
H,  as  respects  the  pole,  when  thus  examined  semi-annu- 
ally.  It  follows,  therefore,  that  the  diameter  of  the  earth's 
orbit  is  wholly  invisible  at  those  distances. 

Again,  let  E  F  I  G,  Fig.  359,  represent  the  orbit  of  the 
earth,  and  K  any  fixed  star,  it  is  obvious  that  when  the 
earth  is  at  G  the  star  would  be  seen  by  G  K,  and  refer- 
red to  the  point,  i;  when  the  earth  is"  at  F  it  would  be 
seen  by  F  K,  and  referred  to  h,  and  the  angle  i  K  h,  which 

Have  the  stars  any  diurnal  parallax  ?    What  must  be  the  appearance  of 
r  sun  to  them  ?    Explain  the  illustrations  given  in  Figs.  358  and  359  re- 
specting parallax. 


ANNUAL   PARALLAX. 


349 


Fig.  359. 


is  equal  to  F  K  G,  would  be  the  annual  parallax,  or  the 
angle  under  which  the  earth's  orbit  would  be  seen  from 
the  star.  But  though  this  is  190  millions  of  miles,  so  im- 
mense is  the  distance  at  whrch  the  fixed  stars  are  placed 
that  it  is  wholly  imperceptible. 

In  a  few  instances,  however,  an  annual  parallax  has 
been  discovered.  Thus,  in  the  star  61  Cygni,  amounts  to 
about  one  third  of  a  second.  The  distance  of  the  near- 
est fixed  star  is,  therefore,  enormously  great. 

The  stars  are  not  scattered  uniformly  over  the  vault  of 

Have  any  stars  an  annual  parallax  ? 


350 


THE    MILKY    WAY. 


heaven,  but  appear  arranged  in  collections  or  groups. 

Just  as  the  planets  and 
their  satellites  make  up, 
with  our  sun,  one  little 
system,  so  too  do  suns 
grouped  together  form 
colonies  of  stars.  The 
milky  way,  Fig.  360, 
which  is  the  group  to 
which  we  belong,  consists 
of  myriads  of  such  suns, 
bound  together  by  mutual 
attractive  influences.  In 
this  S  may  represent  the 
position  of  the  solar  sys- 
tem, and  the  stars  will  ap- 
pear more  densely  scat- 
tered when  viewed  along 
S  p,  than  along  S  m,  S  n, 
S  c.  But  in  other  por- 
tions of  the  heavens  are 
discovered  small  shining 
spaces — nebulce,  as  they 
are  called — which,  uncle J 
powerful  telescopes,  ar 
resolved  into  myriads 
stars,  Fig.  361,  so  far  off 
that  the  human  eye,  when 
unassisted,  is  wholly  una- 
ble to  individualize  them, 
and  catches  only  the  faint 
gleam  of  their  collected 
lights.  Of  these  great 
numbers  are  now  known. 
Such,  therefore,  is  the 
system  of  the  world.  A 
planet,  like  Jupiter,  with 
his  attendant  moons,  is,  as 
it  were,  the  point  of  commencement ;  a  collection  of 
such  opaque  bodies  playing  round  a  central  sun  is  a  fur- 
ther advance — a  system  of  suns,  such  as  form  the  more 


•a 

i 


What  are  nebulae  ?     What  is  the  milky  way  ? 


351 


352  THE    UNIVERSE. 

brilliant  objects  of  our  starry  heavens — and  thousands  of 
such  nebulae  which  cover  the  skies  in  whatever  direction 
we  look.  These,  taken  altogether,  constitute  the  UNI- 
VERSE— a  magnificent  monument  of  the  greatness  of  God, 
and  an  enduring  memento  of  the  absolute  insignificance 
of  man. 

But  though  the  universe  is  the  type  of  Immensity  and 
Eternity,  we  are  not  to  suppose  that  it  is  wholly  un- 
changeable. From  time  to  time  new  stars  have  sudden- 
ly blazed  forth  in  the  sky,  and  after  obtaining  wonderful 
brilliancy  have  died  away — and  also  old  stars  have  disap- 
peared. Recent  discoveries  have  shown  that  the  light  of 
very  many  is  periodic — that  it  passes  through  a  cycle  of 
change  and  becomes  alternately  more  and  less  bright  in 
a  fixed  period  of  days.  These  intervals  differ  in  differ- 
ent cases,  and  probably  all  are  affected  in  the  same  way. 
There  is  abundant  geological  evidence  to  show  that  the 
light  and  heat  of  our  sun  were  once  far  greater  than  now — 
the  luxuriant  vegetation  of  the  secondary  period  could  only 
have  arisen  in  a  greater  brilliancy  of  that  orb.  The  sun, 
then,  is  one  of  these  periodic  stars. 

The  alternate  appearance  and  disappearance  of  some 
of  the  new  stars  may  arise  from  their  orbitual  motion. 
Thus,  suppose  E  the  earth,  and  A  B  C  D  the  orbit  of  such 

Fig.  362. 


K 


a  star.  If  the  major  axis  of  this  orbit  be  nearly  in  the 
direction  of  the  eye,  as  the  star  approaches  to  A,  it  will 
rapidly  increase  in  brilliancy,  and  perhaps  become  wholly 
invisible  at  the  distant  point  C.  Such  a  star  should,  there- 

What  is  the  structure  of  the  Universe  ?  What  changes  have  been  ob- 
served in  the  light  of  some  stars  ?  Is  there  reason  to  believe  that  the  sun 
is  a  periodic  star  ?  Explain  the  probable  cause  of  the  phenomena  of  new 
stars. 


NEBULAR    HYPOTHESIS.  353 

fore,  be  periodical ;  and  that  this  is  the  case  there  is  rea- 
son to  believe  as  respects  one  which  appeared  in  the  years 
945,  1264,  1572,  in  the  constellation  of  Cassiopeia.  Its 
period  seems  to  be  319  years. 

Among  the  nebulae  there  are  some  which  powerful  tel- 
escopes fail  to  resolve  into  stars — a  circumstance  which 
has  caused  some  astronomers  to  suppose  that  they  are 
in  reality  diffused  masses  of  matter  which  have  not  as 
yet  taken  on  the  definite  form  of  globes,  but  are  in 
the  act  of  doing  so.  And,  extending  these  views  to  all 
systems,  they  have  supposed  that  all  the  planetary  and 
stellar  bodies  are  condensations  of  nebular  matter.  To 
this  hypothesis,  although  if  admitted  it  will  account  for  a 
great  many  phenomena  not  otherwise  readily  explained, 
there  are  many  objections :  and  it  is  also  to  be  observed 
that  every  improvement  which  has  been  made  in  the  tel- 
escope has  succeeded  in  resolving  into  stars  nebula3  until 
then  supposed  to  be  unresolvable.  The  inference,  there- 
fore, is.  that  were  our  instruments  sufficiently  powerful  all 
would  display  the  same  constitution. 


LECTURE  LXIX. 

CAUSES  OP  THE  PHENOMENA  OF  THE  SOLAR  SYSTEM. — 
Definitions  of  the  Parts  of  an  Elliptic  Orbit. — Laws  of 
Kepler. — Conjoint  Effects  of  a  Centripetal  and  Projectile 
Force. — Newton's  Theory  of  the  Planetary  Motions. — 
His  Deductions  from  Kepler's  Laws. — Causes  of  Pertur- 
bations. 

HAVING,  in  the  preceding  Lectures,  described  the  con- 
stitution of  the  solar  system,  and  of  the  Universe  gener- 
ally, we  proceed,  in  the  next  place,  to  a  determination  of 
the  causes  which  give  rise  to  the  planetary  movements. 
We  have  to  call  to  mind  that  observation  proves  that  the 
figure  of  the  orbits  of  these  bodies  is  an  ellipse,  the  sun 

What  is  meant  by  the  nebular  hypothesis  ?    What  are  the  objections  to 
it  ?    Describe  the  parts  of  an  elliptic  orbit. 


354  ELLIPTIC    ORBIT. 

being  in  one  of  the  foci.     Thus,  in  Fig.  363,  let  F  be  the 
sun,  A  B  D  E  an  elliptic  orbit,  A  is  the  perihelion,  B  the 

Fig.  3G3. 


aphelion,  F  D  the  mean  distance,  and  JP  C,  which  is  the 
distance  of  the  focus  from  the  center,  the  excentricity ; 
a  line  joining  the  sun  and  the  planet  is  called  the  radius 
vector. 

There  are  three  anomalies — the  true,  the  mean,  and  the 
excentric.  They  indicate  the  angular  distance  of  a  planet 
Fig.  364.  from  its  perihelion,  as  seen  from  the  sun. 
Let  A  p  B  be  the  orbit  of  a  planet,  S  the 
sun,  A  B  the  transverse  diameter  of  the 
orbit,  p  the  place  of  the  planet,  C  the  cen- 
B  ter  of  the  orbit,  with  which  center  let  there 
be  described  a  circle,  A  x  B ;  through  p  draw  x  p  Q,  and 
suppose  that  while  the  real  planet  moves  from  A  to  p, 
with  a  velocity  which  varies  with  its  distance,  an  imagin- 
ary one  moves  in  the  same  orbit  with  an  equable  motion, 
so  that  when  the  real  planet  is  at  p,  the  imaginary  one  is 
at  P,  both  performing  their  entire  revolution  in  the  same 
time.  Then  A  S  p  is  the  true  anomaly,  A  S  P  the  mean 
anomaly,  A  C  a;  the  excentric  anomaly. 

From  an  attentive  study  of  the  phenomena  of  planetary 

What  is  the  radius  vector  ?     What  are  the  true,  the  mean,  and  the  ex- 
centric  anomaly  ? 


KEPLER'S  LAWS.  355 

motions,  Kepler  deduced  their  laws.  These  pass  under 
the  designation  of  the  three  laws  of  Kepler.  They  are — 

1st.  The  planets  all  move  in  ellipses,  of  which  the  sun 
occupies  one  of  the  foci. 

2d.  The  motion  is  more  rapid  the  nearer  the  planet  is 
to  the  sun,  so  that  the  radius  vector  always  sweeps  over 
equal  areas  in  equal  times. 

3d.  The  squares  of  the  times  of  revolution  are  to  each 
other  as  the  cubes  of  the  major  axes  of  the  orbits. 

It  is  one  of  the  fundamental  propositions  of  mechanical 
philosophy  that  a  body  must  forever  pursue  its  motion  in 
a  straight  line  unless  acted  upon  by  disturbing  causes, 
and  any  deflection  from  a  rectilinear  course  is  the  evi- 
dence of  the  presence  of  a  disturbing  force.  Thus,  when 
a  stone  is  thrown  upward  in  the  air,°it  ought,  upon  these 
principles,  to  pursue  a  straight  course,  its  velocity  never 
changing  ;  but  universal  observation  assures  us  that  from 
the  very  first  moment  its  velocity  continually  diminishes, 
and  after  a  time  wholly  ceases — that  then  motion  takes 
place  in  the  opposite  direction,  and  the  stone  falfe  to  the 
surface  of  the  earth.  In  former  Lectures,  we  have  already 
traced  the  circumstances  of  these  motions,  and  referred 
them  to  an  attractive  force  common  to  all  matter,  and  to 
which  we  give,  in  these  cases,  the  name  of  universal  at- 
traction, or  attraction  of  gravitation. 

In  speaking  of  the  motions  of  projectiles,  Lecture 
XX,  it  has  been  shown  that,  under  the  action  of  a 
force  of  impulse  and  a  continuous  force  acting  together, 
not  only  may  a  moving  body  be  made  to  ascend  and  de- 
scend in  a  vertical  line,  but  also  in  curvilinear  orbits,  such 
as  the  parabolic,  the  concavity  of  the  curve  looking  toward 
the  earth's  center,  which  is  the  center  of  attraction.  It 
should  not,  therefore,  surprise  us  that  the  moon,  which 
may  be  regarded  in  the  light  of  a  projectile,  situated  at 
a  great  distance  from  the  earth,  should  pursue  a  curvi- 
linear path,  constantly  returning  upon  itself,  since  such 
must  be  the  inevitable  consequence  of  a  due  apportion" 
ment  of  the  intensity  of  the  projectile  and  central  forces 
to  one  another. 

It  is  the  force  of  gravity  which,  at  each  instant,  makes 

What  are  the  three  laws  of  Kepler  ?  How  may  it  be  proved  that  an  at- 
tractive  force  exists  in  all  the  planetary  masses  ?  What  is  the  result  of 
the  action  of  a  momentary  and  a  continuous  fore*  ? 


356  NEWTON'S  THEORY. 

a  cannon-ball  descend  a  little  way  from  its  rectilinear 
path.  And  it  is  the  same  force  which  also  brings  down 
the  moon  from  the  rectilinear  path  she  would  otherwise 
pursue,  and  makes  her  fall  a  little  way  to  the  earth.  In 
Lecture  XXI,  Fig.  107,  we  have  shown  how,  under  this 
double  influence,  a  circle,  an  ellipse,  or  other  conie  sec- 
tion, must  be  described  ;  and  it  was  the  discovery  of  these 
things  that  has  given  so  great  an  eminence  to  Sir  Isaac 
Newton,  he  having  first  proved  that  it  is  the  same  force 
which  compels  a  projectile  to  return  to  the  earth  and  re- 
tains the  moon  in  her  orbit. 

But  more  than  this,  extending  this  conclusion  to  the 
solar  system  generally,  he  showed  that,  as  the  moon  is 
retained  in  her  orbit  by  the  attractive  influence  of  the 
earth,  so  is  the  earth  retained  in  hers  by  the  attractive 
influence  of  the  sun.  And  taking  the  laws  of  Kepler 
as  facts  established  by  observation,  he  proved,  from  the 
equable  description  of  areas  by  the  radius  vector,  that 
the  force  acting  on  the  planets  and  retaining  them 
in  their  orbits  must  be  directed  to  the  center  of  the 
sun.  From  Kepler's  first  law  of  the  description  of  ellip- 
tic orbits  with  the  sun  in  one  of  the  foci,  he  deduced  the 
law  of  gravitation  or  of  central  attraction  generally — 
that  is,  that  the  force  of  attraction  on  any  planetary  body 
is  inversely  proportional  to  the  square  of  its  distance 
from  the  sun.  And  from  Kepler's  third  law  that  the 
squares  of  the  times  of  revolution  are  as  the  cubes  of 
the  major  axes,  he  proved  that  the  force  of  attraction  is 
proportionate  to  the  masses. 

The  progress  of  knowledge  from  the  time  of  Newton 
until  now  has  only  served  to  establish  the  truth  of  these 
great  discoveries,  and  far  from  restricting  them  to  our  own 
solar  system,  has  shown  beyond  doubt  that  they  apply 
throughout  the  universe.  The  revolutions  of  the  double 
stars  round  one  another  are  consequences  of  the  same 
laws  which  determine  the  orbitual  movements  of  the  sat- 
ellites of  Jupiter  round  their  primary,  or  of  Jupiter  him- 
self round  the  sun.  I 

Even  those  outstanding  facts  which,  at  an  earlier  pe- 
riod, seemed  to  lend  a  certain  degree  of  weight  against 

How  may  this  reasoning  be  applied  to  the  moon  ?  How  to  the  solar 
system  generally  ?  What  did  Newton  deduce  from  Kepler's  laws '(  Does 
the  same  theory  apply  beyond  the  solar  system  ? 


NEWTON'S   THEORY.  357 

the  full  operation  of  the  theory  of  Newton  have,  one 
after  another,  become  illustrations  of  its  truth  as  they 
have  in  succession  become  better  understood. 

Thus,  for  example,  the  deviations  which  the  moon  ex- 
hibits from  a  truly  elliptic  orbit  in  her  passage  round  the 
earth,  and  which  at  first  sight  might  seem  to  bear  against 
Newton's  theory,  are,  when  properly  considered,  the  in- 
evitable consequences  of  it.  If  the  motions  of  the  moon 
were  determined  by  the  influence  of  the  earth's  attrac- 
tion only,  her  orbit  must  be  a  perfect  ellipse,  always  in 
the  same  plane,  and  without  any  retrogradation  of  the 
nodes.  But  observation  shows  that  this  is  not  the  case; 
and,  in  reality,  Newton's  theory  could  have  predicted 
what  is  actually  the  fact ;  for  the  moon  is  not  alone  under 
the  influence  of  the  earth,  but,  like  the  earth,  simulta- 
neously under  the  influence  of  the  sun.  In  her  monthly 
revolution  her  distance  alternately  varies  from  the  latter 
body  by  nearly  half  a  million  of  miles,  in  her  opposition 
being  farther  off,  and  in  her  conjunction  being  nearer  to 
him.  The  law  of  the  inverse  squares,  therefore,  comes 
to  apply ;  and  the  result  must  be  in  some  positions  an  ac- 
celeration, and  in  some  a  retardation  of  her  motion.  And, 
as  her  orbit  is  not  coincident  with  the  plane  of  the  eclip- 
tic, the  action  of  the  sun  must  necessarily  tend  to  draw 
her  out  of  that  plane,  and  thus  produce  the  retrograde 
revolution  of  her  nodes. 

The  summation  of  the  theory  of  Newton,  therefore, 
comes  to  this,  that  all  masses  of  matter  in  the  universe 
attract  one  another  with  forces,  the  intensities  of  which, 
at  equal  distances,  are  proportional  to  their  masses,  and 
which,  with  equal  masses,  at  different  distances,  are  in- 
versely proportional  to  the  squares  of  those  distances. 
That  the  elliptical  motion  results  from  a  primitive  projec- 
tile impulse  impressed  on  the  heavenly  bodies  by  the 
Creator,  conjoined  with  the  continuous  agency  of  the  at- 
tractive force.  Upon  these  principles  every  variety  of 
motion  exhibited  by  the  celestial  bodies  may  be  expound- 
ed, whether  it  be  the  almost  circular  path  described  by 

What  should  the  moon's  motion  be  if  under  the  influence  of  the  earth 
alone?  What  is  it  in  reality?  To  what  cause  is  this  due?  How  is  it 
that  the  sun  impresses  changes  of  velocity  on  the  moon's  motion,  and 
makes  her  nodes  retrograde  ?  What  are  the  principal  points  in  Newton's 
theory  ? 


358  THE    TIDES. 

the  moon  round  the  earth,  the  excessively  eccentric  ellip- 
ses described  by  some  comets  round  the  sun,  or  the  para- 
bolic or  hyperbolic  orbits  followed  by  others  ;  in  which  case 
they  enter  our  system  but  once,  and,  having  passed  their 
perihelion,  leave  it  forever.  Moreover,  these  principles 
yield  us  a  clear  explanation  of  other  facts — at  first  not  ap- 
parently connected  with  them — such  as  perturbations  gen- 
erally, the  figure  of  the  earth,  and  the  tides,  which  are 
caused  in  the  sea  by  the  conjoint  influence  of  the  sun 
and  the  moon,  as  we  shall  now  proceed  to  explain. 


LECTURE  LXX. 

THE  TIDES. — Flood  and  Ebb-Tide. — Spring  and  Neap- 
Tide. — General  Phenomena  of  the  Tides. —  Connection 
with  the  Position  of  the  Moon. — Effects  of  the  Diurnal 
Rotation. — Action  of  the  Sun. — Local  Tidal  Effects. 

BY  the  tide  we  mean  an  elevation  and  depression  of 
the  waters  of  the  sea,  occurring  twice  during  the  course 
of  a  day.  For  about  six  hours  the  sea  flows  from  south 
to  north  ;  it  then  remains  stationary  for  about  a  quarter  of 
an  hour,  then  ebbs  in  the  opposite  direction  for  about 
six  hours,  is  then  stationary  again  for  a  quarter,  and  then 
recommences  to  flow.  To  this  elevation  and  depression 
the  names  of  flood  and  ebb  are  given.  And  as  the  ab- 
solute height  of  the  tides  varies,  as  we  shall  presently 
see,  at  different  times,  the  highest  tide  is  called  a  spring- 
tide, and  the  lowest  a  neap-tide. 

The  space  of  time  occupied  in  one  flow  and  ebb  is 
about  twelve  hours  and  twenty-five  minutes.  There  are, 
therefore,  two  tides  during  one  lunar  day — or,  what  is  the 
same,  every  time  the  moon  crosses  the  meridian,  whether 
superior  or  inferior,  there  is  a  tide  ;  but  the  actual  time 
of  high  water  out  at  sea  is  not  at  the  instant  when  the 
the  moon  is  upon  the  meridian,  but  about  two  hours 
later. 

Mention  some  other  phenomena  which  this  theory  explains.  What  is 
meant  by  the  tide  ?  Describe  the  principal  phenomena  of  it.  What  is  a 
spring  and  what  a  neap-tide?  What  time  is  occupied  in  one  ebb  and 
flow  ?  What  is  the  position  of  the  moon  at  the  time  of  high  water  ? 


ACTION    OF    THE    MOON.  359 

There  can  be  no  doubt  that  it  is  the  influence  of  this 
luminary  that  is  the  cause  of  the  tides.  Her  attraction 
must  necessarily  render  those  portions  of  the  sea  that  are 
immediately  beneath  her  of  less  weight,  and,  by  the  laws 
of  hydrostatics,  they,  therefore,  must  rise  until  an  equi- 
librium be  established.  But  on  those  points  which  are 
in  quadrature  with  her,  the  effect  of  her  action,  by  reason 
of  its  obliquity,  is  to  render  them  heavier ;  and,  as  re- 
spects those  which  are  diametrically  opposite  to  her,  on 
the  other  side  of  the  earth,  she  must  exert  on  them  a  less 
powerful  attraction  than  she  does  on  the  earth's  center, 
because  they  are  more  remote  than  it.  From  this  ine- 
quality and  obliquity  of  the  moon's  action  there  must  ne- 
cessarily ensue  an  elevation  on  those  parts  of  the  sea 
which  are  immediately  beneath  her,  and  also  on  those 
which  are  on  the  opposite  side  of  the  earth ;  but  on  those 
positions  which  are  situated  at  right  angles  to  these  points 
there  must  be  a  depression. 

When  these  considerations  are  combined  with  the  fact 
of  the  diurnal  rotation  of  the  earth  on  its  axis  it  will  be 
perceived  that  the  tide  thus  formed  must  necessarily 
follow  the  apparent  course  of  the  moon,  and  that  in  any 
given  locality  there  must  be  high  water  and  low  water 
twice  in  every  lunar  day. 

In  Fig.  365,  let  a  b  c  d  be  the  earth  and  M  the  moon ; 
and  let  the  shaded  line  sur-  Fig.  365. 

rounding  the  earth  on  all  sides 
represent  its  surface  as  cover- 
ed with  a  uniform  sea.  Now, 
as  the  attractive  force  of  the 
moon  varies  inversely  as  the 
squares  of  the  distance,  it  must 
be  strongest  at  a,  more  feeble 
at  b  and  d,  and  still  more  fee- 
ble at  c.  Under  this  attractive 
influence  the  waters  at  a  will 
necessarily  rise,  and  the  sea, 
losing  its  perfectly  spherical  shape,  will  assume  that  of  an 

To  what  cause  is  the  elevation  of  the  water  due  ?  What  is  the  moon's 
action  on  those  parts  of  the  earth  nearest  and  most  distant  from  her? 
What  on  those  parts  at  quadrature  with  them?  Why  does  the  tide  fol- 
low the  apparent  course  of  the  moon  I  Describe  the  illustration  given 
in  Fig.  365. 


360  ACTION    OF    THE    MOON. 

ellipsoid — or,  in  other  words,  a  tide  will  form  upon  it. 
Arid,  as  the  center  of  the  earth  at  o  is  more  attracted  than 
the  point  c,  because  it  is  nearer  the  moon,  it  will  advance 
toward  the  moon  more  than  will  the  water  at  c  ;  and  at 
that  point  an  elevation  forms,  so  that  at  a  and  at  c  there 
will  be  high  water.  But  as  respects  the  points  I  and  d, 
which  are  at  the  quadratures,  the  force  of  the  moon,  by 
reason  of  the  obliquity  under  which  it  is  acting,  may  there 
be  decomposed;  and  if  this  be  done  it  will  be  seen  that 
a  part  of  that  force  is  expended  in  increasing  the  weight 
of  particles  in  those  positions — or,  in  other  words,  making 
them  tend  more  powerfully  toward  the  center  of  the  earth. 
Under  these  circumstances,  therefore,  there  being  a  di- 
minished weight  at  a  and  c,  and  an  increased  one  at  b  and 
d,  the  spherical  form  of  the  shell  of  water  is  lost;  there  is 
an  elevation  at  a  and  c  and  a  depression  at  b  and  d, 
high  water  at  the  former  and  low  water  at  the  latter 
places.  And  as  the  earth  rotates  on  her  axis  so  as  to 
bring  the  moon  upon  the  meridian  in  about  twenty-four 
hours  and  fifty  minutes,  in  that  space  of  time  there  must 
be  two  tides.  Were  it  not  for  this  diurnal  rotation  there 
would  only  be  two  sets  of  tides  in  a  month. 

As  a  movement  communicated  to  the  waters  cannot 
cease  at  once,  and  as  the  elevation  of  the  water  is  moved 
away  from  the  moon  by  the  earth's  revolution,  the  water 
still  continues  to  rise  for  a  certain  time,  although  the  point 
of  elevation  is  no  longer  immediately  beneath  the  moon. 
So  the  time  of  high  water  is  not  coincident  with  the  pas- 
sage of  the  moon  over  the  meridian,  but  occurs  somewhat 
later. 

In  the  same  way  that  the  moon  thus  produces  tides  in 
the  sea,  so,  too,  must  the  sun.  And,  as  his  attractive 
force  is  much  greater  than  hers,  it  might,  at  first  sight, 
appear  that  he  should  give  rise  to  far  higher  tides.  But 
his  great  distance  makes  a  wide  difference  in  the  result ; 
so  that,  in  point  of  fact,  the  moon  is  almost  three  times 
as  energetic  as  he  is.  We  have  shown,  in  Fig.  365,  how 
much  the  obliquity  of  the  moon's  action  on  the  points  in 
quadrature  has  to  do  with  the  final  effect.  Not  so  with 
the  sun.  His  influence  on  the  different  parts  of  the  sea 

Why  is  not  the  time  of  high  water  coincident  with  the  moon's  meridian 
passage  ?  Does  the  sun  act  in  the  same  manner  as  the  moon  ?  What  differ- 
ence is  there  between  him  and  the  moon  as  respects  obliquity  of  action  ? 


SPRING-TIDES.  361 

takes  place  almost  in  parallel  lines,  and,  therefore,  the 
effect  becomes  feeble.     Still  the  sun  does  each  day  pro- 
duce two  tides  as  the  earth  revolves,  though  they  are  tides 
of  much  less  magnitude  than  the  lunar  ones. 
In  Fig.  366  let  E  be  the  earth,  M  the  moon,  and  S  the 

Fig.  366. 


sun ;  and,  as  before,  let  the  shaded  line  round  the  earth 
represent  a  uniform  sea.  Now,  it  is  obvious  that  when 
these  bodies  are  in  the  position  represented  in  the  figure 
the  action  of  both  will  coincide,  and  they  will  jointly 
raise  a  higher  tide.  Also  the  same  must  take  place  when 
the  sun  being  at  S  the  moon  is  at  M'.  But  these  posi- 
tions are  evidently  those  of  the  new  and  the  full  moon, 
and.  therefore  at  these  times  the  highest  tides — spring- 
tides— occur. 

In  this  case  the  time  of  the  greatest  elevation  of  water 
does  not  coincide  with  that  of  the  passage  of  both  lumi- 
naries over  the  meridian,  but  occurs  some  time  later.  A 
certain  period  is  required  in  order  to  communicate  motion 
to  the  mass  of  the  water. 

* 

From  what  does  this  arise  ?  How  many  solar  tides  are  there  in  a  day  ? 
Describe  the  illustration  given  in  Fig.  366.  At  what  times  do  spring- 
tides consequently  occur  ?  Does  the  time  of  greatest  elevation  coincide 
with  that  of  the  passage  of  both  luminaries  over  the  meridian  ? 

3 


362  NEAP-TIDES. 

Now,  let  the  luminaries  be  as  is  represented  in  Fig. 
3G7,  where  S  is  the  sun,  E  the  earth,  surrounded  by  its 
ocean,  and  M  or  M'  the  moon  in  either  of  the  quadra- 

Fiff.  367 


tures.  In  this  position  the  effect  of  one  of  the  bodies 
counteracts  that  of  the  other.  Those  points  which  in  the 
solar  tide  would  be  high  water  are  low  water  for  the 
lunar  tide.  Under  these  circumstances  the  sea  departs 
much  less  from  its  undisturbed  position,  and  the  tidal 
movements  are  less.  This  condition  of  things  corresponds 
to  the  neap-tides.  Neap-tides,  therefore,  occur  when  the 
moon  is  in  her  quadratures. 

The  actual  rise  of  the  tide  differs  very  much  in  differ- 
ent places,  being  greatly  determined  by  local  circum- 
stances. Thus,  in  the  bay  of  Fundy  it  sometimes  rises 
as  high  as  eighty  feet ;  in  the  West  Indies  it  is  said  to  be 
scarcely  more  than  from  ten  to  fifteen  inches.  These 
modifications  arise  from  a  great  variety  of  disturbing 
causes,  such  as  the  interference  of  successive  tide-waves, 
the  configuration  of  coasts,  the  prevalence  of  winds,  &c. 
In  inland  seas  and  lakes  there  are  no  tides,  because  the 
moon  acts  equally  over  all  their  surface. 

How  is  it  that  neap-tides  occur  ?  What  local  atrcu instances  affect  the 
tides. 


FIGURE    OF   THE    EARTH.  363 


,f  -:          LECTURE  LXXI. 

THE  FIGURE  AND  MOTIONS  OF  THE  EARTH. — Astronomi- 
cal Appearances  connected  with  the  Earth's  Figure. — 

.  Determination  of  the  Length  of  a  Degree. — Actual  Di- 
mensions of  the  Earth. — Amount  of  Oblateness. — Diurnal 
Rotation  proved  by  the  Oblateness. — Annual  Motion 
Round  the  Sun  proved  frtim  Aberration  of  the  Stars.—- 
Determination  of  Latitudes. — Determination  of  Longi- 
tudes. 

FROM  considerations  connected  with  the  appearance  of 
objects  at  sea,  or  where  there  is  an  unobstructed  view  of 
the  horizon,  we  have  already  deduced  the  fact  of  the 
globular  figure  of  the  earth.  If  any  doubt  remained  on 
this  point  it  would  be  entirely  removed  by  the  well 
known  circumstance  that,  on  very  many  occasions,  navi- 
gators have  sailed  round  the  world. 

An  observer  situated  near  the  equator  sees  the  north 
polar  star  upon  the  horizon,  but  as  he  travels  toward  our 
latitudes  the  star  seems  to  rise  correspondingly  in  the 
sky,  and  if  he  could  pursue  his  journey  far  enough  would 
finally  |?e  over  his  head.  .  In  this  fact  we  have  another 
proof  of  the  spherical  figure  of  the  earth ;  for,  were  it  a 
flattened  surface  or  a  plane,  such  a  change  in  the  position 
of  the  stars  could  not  take  place. 

Seeing,  therefore,  that  our  earth  is  of  a  spherical  figure, 
it  may  easily  be  demonstrated  that  for  every  degree  that 
we  go  northward  upon  its  surface,  the  north  pole  is  ele- 
vated a  degree  above  the  horizon.  This  observation  fur- 
nishes us  with  a  ready  means  of  determining  the  actual 
magnitude  of  our  planet. 

"  For  this  purpose  it  would  be  only  necessary  to  select 
two  positions  on  the  same  meridian,  at  which  there  was 
a  difference  in  the  elevation  of  the  pole  of  one  degree ; 
the  distance  between  those  places,  if  measured,  would  be 
_.i_  part  of  the  entire  circumference  of  the  earth.  The 
problem  of  determining  the  dimensions  of  the  earth  re- 

What  simple  facts  afford  proof  of  the  globular  figure  of  the  earth  ?  On 
what  principle  may  we  determine  its  magnitude  ? 


364  FIGURE    OF   THE    EARTH. 

solves  itself,  therefore,  into  the  measurement  of  the  length 
of  a  degree. 

Measurements  effected  on  these  principles  give  for  the 
circumference  of  the  earth  24,880  miles,  from  which  we 
deduce  its  diameter  to  be  7920.  _;  ' 

But  such  measurements  have  also  proved  that  the 
value  of  a  degree  is  not  the  same  in  all  places  ;  for,  as  we 
leave  the  equator  and  go  toward  the  poles,  the  length  of 
the  degree  becomes  greater.  This,  therefore,  shows  that 
though  the  general  figure  of  the  earth  is  spherical,  yet  it 
is  not  a  perfect  sphere  :  a  perfect  sphere  must  have  its 
degrees  of  uniform  length;  and  such  an  increase  in  the 
length  of  the  degree  can  be  explained  on  one  principle 
only — that  the  earth  is  flattened  toward  the  poles. 

The  analogies  of  other  bodies  in  the  solar  system  illus- 
trate this  explanation  :  both  the  great  planets,  Jupiter  and 
Saturn,  are  flattened  toward  the 
poles,  the  former  having  his 
polar  diameter  shorter  than  his 
equatorial  -Jy,  and  the  latter  -Jy. 
Such  an  oblate  spheroidal  figure 
is  presented  to  us  in  the  case  of 
an  orange.  This  flattening  is 
seen  in  Fig.  368,  where  N  S  is 
the  polar  diameter.  From  trig- 
onometrical measurements  of  the 
surface  of  the  earth,  it  is  infer- 
red that  the  flattening  is  about  ^IF,  or  that  the  polar  is 
shorter  than  the  equatorial  diameter  by  about  twenty- 
six  miles.  The  earth  may  be  regarded,  therefore,  as 
having  a  zone  or  projecting  ring  upon  its  surface,  which 
has  a  maximum  thickness  immediately  under  the  equator. 
From  the  effect  of  gravity  varying  as  the  inverse  square 
of  the  distance  from  the  earth's  center,  and  from  the 
figure  of  the  earth,  its  polar  regions  being  nearer  the 
center  than  its  equatorial,  the  weight  of  bodies  must 
change  as  we  pass  from  the  equator  to  the  poles.  Now, 
the  number  of  vibrations  which  a  pendulum  of  given 

What  are  the  circumference  and  diameter  of  the  earth  in  miles  ?  Is  the 
length  of  the  degree  the  same  in  all  places?  What  follows  from  this  as 
respects  the  earth's  figure  ?  Is  this  conclusion  verified  in  the  case  of 
other  planets?  By  how  much  does  the  equatorial  exceed  the  polar 
diameter  ? 


CAUSE    OF    OBLATENESS. 


3G5 


length  makes  in  a  given  time  depends  on  the  intensity  of 
gravity;  and  when  one  of  these  instruments  is  examined, 
it  is  found  to  beat  more  rapidly  as  it  approaches  the 
poles.  This  phenomenon  has  already  been  discussed  in 
Lecture  XXV,  and  referred  to  its  proper  cause.  From 
the  oscillations  of  a  pendulum  the  figure  of  the  earth 
may  be  determined. 

From  a  variety  of  facts,  as  well  as  from  the  general 
analogy  of  every  body  in  the  solar  system,  the  sun  him- 
self not  excepted,  we  have  deduced  the  fact  of  the  daily 
revolution  of  the  earth  on  her  own  axis.  It  is  the  prop- 
erty of  all  true  philosophical  theories  to  meet  with  con- 
firmation under  circumstances  where  we  might  have  been 
little  likely  to  have  expected  it.  And  so,  with  the  diurnal 
revolution  of  the  earth,  it  might  be  demonstrated  from 
the  oblate  spheroidal  figure,  had  we  no  other  proof  of  it; 
but  having  such  proofs  in  abundance,  this  comes  as  a 
corroborative  illustration  ;  for,  as  the  earth  revolves  on 
her  axis,  it  must  needs  follow  that  she,  like  all  other 
revolving  bodies,  gives  rise  to  a  centrifugal  force  which 
is  as.  the  square  of  the  velocity  of  rotation.  At  the  equa- 
tor where  the  speed  of  rotation  is  the  greatest,  and  a 
given  point  passes  through  25,000  miles  in  24  hours — that 
is,  with  more  than  the  speed  of  a  cannon-ball — the  centri- 
fugal force  is  at  a  maximum,  and  from  this  point  it  de- 
clines until  at  the  poles  it  ceases.  Let  us  call  to  mind 
the  experiment  formerly  ex- 
hibited by  the  machine  rep- 
resented in  Figure  369,  in 
which  the  two  brass  hoops, 
a  b,  bent  into  a  circular  form 
when  they  are  made  to  re- 
volve rapidly  by  turning  the 
handle  of  the  multiplying- 
wheel,  depart  from  their  cir- 
cular shape  and  bulge  out 
into  that  of  an  ellipse  ;  and 
according  as  the  velocity  of. 
rotation  is  greater  so  is  the 
elliptical  figure  better  mark- 
How  does  this  affect  the  weight  of  bodies  and  the  beating  of  pendulums  ? 
How  does  the  figure  of  the  earth  prove  the  fact  of  its  diurnal  rotation  ? 
What  is  the  relation  of  the  centrifugal  force  at  the  equator  and  at  the  poles  ? 


Fig.  369. 


366          ABERRATION  OF  THE  STARS. 

ed.  It  is  then  the  diurnal  revolution  of  the  earth  on  her 
axis  which  has  given  her  a  shape  flattened  at  the  poles, 
and  in  the  same  way  in  the  case  of  all  the  other  great 
planets,  the  flattening  is  immediately  dependent  on  the 
velocity  of  rotation. 

We  have  already  given  so  many  proofs  of  the  earth's 
orbitual  motion  round  the  sun,  that  any  thing  further  might 
seem  unnecessary.  I  shall,  however,  explain  what  is 
meant  by  the  aberration  of  the  fixed  stars,  not  only  from 
its  intimate  connection  with  one  of  the  fundamental  facts 
in  optical  science — the  progressive  motion  of  light — but 
also  from  its  being  a  striking  exemplification  of  the  truth 
here  more  immediately  under  consideration,  the  transla- 
tory  movement  of  the  earth  round  the  sun. 

Let  A  B  C  D,  Fig.  370,  be  the  earth's  orbit,  and  E  any 
given  star.  When  the  earth  is  at  A,  the  star  will  be  seen 
in  the  line  A  E,  and  referred  on  the  sphere  of  the  heav- 
ens to  G.  When  the  earth  has  passed  through  one  half 
of  her  orbit,  and  arrived  at  C,  the  star  will  be  seen  in  the 
line  C  E,  and  referred  to  F.  From  what  has  already  been 
said  in  relation  to  parallax,  it  will  be  understood  that  this 
shifting  of  the  star  from  G  to  F  depends  on  its  having  a 
measurable  distance  from  the  earth. 

With  a  view  of  determining  the  parallax  of  one  of  the 
stars,  and  consequently  its  distance  from  the  earth,  two  as- 
tronomers during  the  last  century  commenced  observa- 
tions founded  on  these  principles  ;  and  selecting  the  star  y 
in  the  constellation  Draco,  examined  its  position  for  the 
several  months  in  the  year.  Thus,  for  example,  the  earth 
being  at  C  in  the  month  of  September,  and  the  star  refer- 
red to  F :  six  months  afterward — that  is  in  March — the 
earth  being  at  A,  they  expected  the  star  would  change  its 
position,  and  be  referred  to  G  ;  but,  to  their  surprise,  they 
found  the  movement  was  in  precisely  the  opposite  direc- 
tion, the  star  being  seen  at  K,  the  movement  being  from 
F  to  K,  instead  of  from  F  to  G.  This  is  what  is  known 
as  "the  aberration  of  the  fixed  stars,"  and  its  explanation 
depends  on  the  fact  that,  owing  to  light  moving  pro- 
gressively and  not  instantaneously,  and  the  eye  of  the  ob- 

Why  is  the  figure  of  a  planetary  body  thus  connected  with  its  rotation 
on  its  axis  ?  How  was  the  aberration  of  the  fixed  stars  first  discovered  f. 
What  is  the  direction  of  the  apparent  motion  of  a  star  compared  with 
what  it  should  be  from  parallax  1 


ABEEEATION    OP    THE    FIXED    STARS.  367 


Fig.  370. 


server  accompanying  the  earth  in  her  orbit,  the  position 
of  the  stars  is  not  the  same  as  what  it  would  be  were  the 
earth  at  rest.  The  cause  of  this  has  been  explained  in 
Lecture  XXXVI. 

It  is  constantly  observed  of  true  physical  theories  that 
they  afford  explanations  of  facts,  and,  on  the  other  hand, 
receive  illustrations  from  facts  with  which,  at  first  sight, 

How  is  this  motion  explained  ? 


368  LATITUDE  AND  LONGITUDE. 

they  did  not  seem  to  be  connected.  The  aberration  of 
the  fixed  stars  proves  two  of  the  most  prominent  physical 
theories  with  which,  at  the  first  sight,  it  does  not  seem  to 
be  in  the  slightest  degree  allied — the  progressive  motion 
of  light,  and  the  earth's  motion  round  the  sun. 

It  is  often  a  most  important  problem  to  determine  the 
position  of  a  given  point  on  the  earth's  surface.  Navi- 
gation essentially  depends  on  determining  with  precision 
the  place  of  a  ship  at  sea.  To  effect  this  two  problems 
have  to  be  solved — to  find  the  latitude  and  also  the  longi- 
tude. 

The  former  of  these  is  the  more  easily  determined  of 
the  two.  It  may  be  clone  in  several  different  ways :  such 
as  by  the  zenith  distance  of  stars,  meridian  altitudes  of 
the  sun,  or  the  east  and  west  passage  of  a  star  through  the 
prime  vertical.  The  latitude  of  a  place  being  the  eleva- 
tion of  the  pole  above  the  horizon,  among  other  methods 
it  may,  therefore,  be  ascertained  by  finding  the  greatest 
and  least  altitudes  of  a  circurnpolar  siar ,  naif  the  sum  of 
those  altitudes  being  equal  to  the  latitude.  Of  course, 
latitude  is  of  two  kinds — northern  and  southern.  In  any 
given  instance,  we  indicate  which  by  the  letter  N  or  S. 

In  like  manner,  there  are  several  ways  by  which  the 
longitude  of  a  place  may  be  determined.  Longitude  is 
estimated  by  the  number  of  degrees  upon  the  equator,  in- 
tercepted between  the  meridian  of  the  place  of  observa- 
tion and  the  meridian  of  some  other  place,  taken  as  a 
standard  or  starting-point,  such  as  the  meridian  of  Green- 
wich or  Washington.  Since  a  given  point  on  the  earth 
makes  one  complete  revolution  of  three  hundred  and  sixty 
degrees  in  twenty-four  hours,  it  will  describe  in  one  hour 
fifteen  degrees.  In  two  places  which  are  fifteen  degrees 
of  longitude  apart,  the  sun  comes  on  the  meridian  of  the 
more  westerly  one  hour  later  than  on  that  of  the  other. 
To  find  the  longitude,  therefore,  is  to  find  the  difference 
of  the  time  of  day  between  the  place  of  observation  and 
that  taken  as  the  standard.  For  this  purpose  chronome- 
ters are  employed. 

The  eclipses  of  Jupiter's  satellites  and  occultations  of 
stars  by  the  moon,  are  predicted  in  appropriate  almanacs, 

How  is  the  position  of  a  place  on  the  earth  determined  ?  How  may  the 
latitude  be  found  ?  How  is  longitude  estimated  ?  How  may  it  be  found  ? 
What  use  is  made  of  the  eclipses  of  Jupiter's  satellites  and  occultations? 


PERTURBATIONS.  369 

with  the  exact  moment  of  their  occurrence  at  the  stand- 
ard meridian.  It  is,  therefore,  only  necessary  to  mark  the 
time  at  which  one  of  these  occurs  at  the  place  of  obser- 
vation, and  the  difference  of  the  times  gives  the  longi- 
tude. 5 


LECTURE  LXXII. 

OF  PERTURBATIONS.— Action  of  Three  Bodies. —  Variation 
from  an  Elliptic  Orbit.— Inequalities  of  the  Moon.— 

Conjoint  Action  of  the  Sun  and  Earth  upon  the  Moon. 

Annual  Equation. — Change  in  Position  of  the  Nodes. — 
Precession  of  the  Equinoxes. — Discovery  of  the  Planet 
Neptune. 

ON  the  principles  of  mechanics  it  may  be  demonstrated 
that  if  a  solitary  planet  revolve  round  a  central  sun,  the 
path  which  it  describes  must  be  an  ellipse,  from  which  it 
would  never  deviate.  But  if  a  second  planet  or  other  at- 
tracting body  be  introduced,  then  it  follows,  as  a  direct 
consequence  of  the  principle  of  universal  gravitation,  that 
disturbance  will  ensue,  and  the  revolving  bodies,  instead 
of  moving  in  exact  ellipses,  will  follow  new  paths  accord- 
ing as  their  relation  of  distance  to  each  other  changes. 

These  results,  which  we  thus  foresee  theoretically,  are 
verified  in  the  heavens.  The  planetary  bodies  of  our  so- 
lar system  do  not,  as  we  have  heretofore  supposed,  pur- 
sue invariable  elliptic  paths  round  the  sun,  but  each  plan- 
et attracts  all  the  rest  in  the  same  way  and  under  the  same 
laws  that  the  sun  attracts  them  all.  His  superior  mass 
predominates,  and  gives  its  general  character  to  the  re- 
sulting movement,  but  the  impression  which  each  one 
makes  upon  its  neighbor  is  plain  enough  to  be  traced. 

To  these  disturbances  the  general  name  of  perturba- 
tions is  given,  and  when  they  occur  between  planets  and 
satellites  the  name  of  inequalities.  They  are  secular  and 
periodical.  In  every  instance  they  compensate  one  an- 
other, so  that  after  a  certain  period  has  elapsed,  the  dis- 

What,  on  the  principles  of  mechanics,  must  be  the  path  of  a  single 
planet  ?     If,  instead  of  two,  there  be  three  bodies,  what  will  be  the  result  ? 
How  does  this  apply  to  the  solar  system  ?     What  is  meant  by  perturba- 
tions and  inequalities  I    Of  what  kinds  are  they  ? 
Q* 


370 


INEQUALITIES    OF    THE    MOON. 


turbances  have  neutralized  themselves,  and  every  thing  is 
brought  back  to  the  original  condition. 

The  inequalities  of  the  moon  arid  the  earth  furnish  us 
with  a  clear  illustration  of  these  principles.  In  her 
monthly  revolution  round  the  earth,  the  moon  alternately 
approaches  to  and  recedes  from  the  sun.  Her  distance 
from  the  earth  being  about  240,000  miles,  her  distance 
from  the  sun  at  conjunction  and  opposition  differs  by  al- 
most half  a  million  of  miles,  and  under  the  law  of  the  in- 
verse squares,  his  attractive  force  upon  her  corresponding- 
ly changes.  When  in  conjunction — that  is,  between  the 
earth  and  the  sun,  his  attraction  acting  more  powerfully 
on  her — she  approaches  toward  him,  and  her  distance 
from  the  earth  therefore  increases  :  when  in  opposition, 
the  earth  being  the  nearer,  is  more  powerfully  attracted, 
and  again  the  distance  between  the  two  is  increased. 
Thus,  let  S,  Fig.  371,  be  the  sun,  E  the  earth,  and  A  D  B 
C  the  orbit  of  the  moon.  If  the  moon  be  at  her  quad- 

Fig.  371. 


\ 

rature,  A,  the  distances  of  the  moon  and  earth  from  the 
sun  are  equal,  and  the  attractive  force  maybe  represented 
by  the  lines  A  S,  E  S.  Draw  A  L  parallel  and  equal  to 
E  S,  and  complete  the  parallelogram  E  A  L  S.  The  force 
A  S  may  be  decomposed  into  two,  A  E  directed  toward 
the  earth's  center  and  A  L.  While  A  L  acts  parallel  to 
E  S,  it  does  not  produce  any  disturbance,  but  A  E  act- 
ing toward  the  earth's  center,  increases  the  weight  or 
gravity  of  the  moon,  and  makes  her  fall  more  toward  the 
earth  :  and  the  same  will  take  place  in  the  other  quadra- 
ture, B. 

For  these  reasons  we  see  that  in  the  moon's  conjunc- 

Give  an  illustration  of  these  principles  in  the  case  of  the  sun,  earth, 
and  moon. 


PERTURBATIONS.  371 

tion  and  opposition  her  gravity  toward  the  earth  is  dimin- 
ished, but  at  the  quadratures  it  is  increased.  So  that  if  we 
were  to  conceive  the  sun  absent,  and  the  moon  revolving 
round  the  earth  in  a  circle,  if  the  sun  were  thfen  intro- 
duced his  influence  would  make  her  describe  an  ellipse, 
the  longest  axis  of  which  would  be  at  the 'quadratures! 
It  may  seem  somewhat  paradoxical  that  the  moon  should 
come  nearest  the  earth  when  her  weight  is  least;  but 
this  is  only  an  incidental  thing  :  it  arises  from  the  cir- 
cumstance that  her  approach  is  the  result  of  the  great 
curvature  of  her  orbit  at  the  quadratures,  and  arises  from 
the  velocity  and  direction  she  has  acquired  in  conjunction 
or  opposition. 

Under  these  circumstances  the  velocity  of  her  motion 
changes.  The  velocity  diminishes  from  conjunction  up 
to  the  first  quadrature,  then  increases  up  to  opposition. 
It  diminishes  again  to  the  second  quadrature,  and  increases 
to  conjunction. 

It  further  follows,  from  the  same  principles,  that,  as  the 
earth  revolves  in  her  eJKptic  orbit  round  the  sun,  at  one 
time  approaching  to  him  and  at  another  receding,  new 
variations  will  arise,  because  the  relative  distances  of  the 
earth,  the  moon,  and  tbe  sun  are  changed,  thus  giving 
rise  to  another  inequality,  which  is  called  the  annual 
equation. 

The  foregoing  explanation  will  set  in  its  proper  light 
the  nature  of  perturbation,  and  show  how  it  necessarily 
arises  from  the  theory  of  gravitation.  The  subject  in  it- 
self is  exceedingly  complicated  in  its  applications,  and  far 
exceeds  the  limits  which  I  can  here  give  to  it.  Connected 
•with  the  foregoing  we  may,  however,  trace  a  second  in- 
stance. The  moon's  nodes,  or  the  points  where  her  orbit 
intersects  the  ecliptic,  undergo  an  annual  change  of  posi- 
tion of  more  than  19°,  making  a  complete  revolution  in  a 
little  more  than  eighteen  years  and  a  half.  This  disturb- 
ance arises  from  the  attraction  of  the  sun  ;  for  as  the 
moon's  orbit  is  inclined  at  an  angle  of  five  degrees  to  the 
ecliptic,  as  she  revolves  round  the  earth  and  approaches 

At  what  periods  is  the  moon's  gravity  to  the  earth  increased  and  at 
what  diminished  ?  What  effect  does  the  sun  exert  on  the  orbit  of  the 
moon?  What  changes  take  place  in  the  moon's  velocity?  What  is  meant 
by  the  annual  equation  ?  What  is  the  cause  of  the  retrogradation  of  the 
moon's  nodes  ? 


372  PRECESSION    OF    THE    EdUINOXES. 

the  plane  of  the  ecliptic,  the  sun's  action  brings  her  down 
more  quickly,  and  makes  her  cross  the  ecliptic  sooner  than 
she  would  otherwise  have  done. 

The  list  of  these  perturbations  to  which  I  shall  now 
allude  explains  the  cause  of  the  precession  of  the  equinoxes. 
At  the  time"  that  names  were  given  to  the  signs  of  the 
zodiac  the  vernal  equinox  coincided  with  the  first  point 
of  Aries.  It  is  now  more  than  thirty  degrees  to  the  west- 
ward ;  for  the  sun  crosses  the  equator  each  year  at  a 
point  fifty  seconds  west  of  that  in  which  he  crossed  it  the 
preceding  year;  and  thus  the  equinoxial  points  will  make 
a  complete  revolution  in  25,867  years,  the  seasons  then 
having  completely  run  through  all  the  months  of  the 
year. 

This  phenomenon  arises  from  the  oblate  figure  of  the 
earth,  resulting  from  her  rotation  upon  her  axis,  the  sun's 
attraction  being  exerted  upon  the  zone  of  matter  which 
surrounds  the  earth  like  a  protuberance  at  the  equator, 
and  tending  to  make  it  approach  the  plane  of  the  ecliptic. 
The  equinoction  points — the  points  where  the  ecliptic 
and  equator  intersect — therefore  recede,  and  the  axis  of 
rotation  of  the  earth  moves  with  a  conical  motion  round 
the  axis  of  the  ecliptic.  The  pole  of  the  earth's  axis 
describes,  therefore,  a  circular  motion  round  the  pole  cf 
the  ecliptic,  completing  its  revolution  in  25,867  years.  In 
successive  ages  the  earth's  pole  points  to  different  stars, 
which  become  pole-stars  in  succession. 

These  examples  may  afford  a  general  idea  of  the  nature 
of  PERTURBATIONS,  and  show  that,  though  they  give  rise 
to  effects  which  might  appear  contradictory  to  the  theory 
of  universal  gravitation,  they  are  in  reality,  as  has  been 
already  observed,  the  necessary  consequences  of  it.  The 
cases  that  we  have  been  considering  are  very  simple  ; 
but  we  can  understand  how  difficult  such  problems  be- 
come where  more  complicated  systems  are  under  investi- 
gation— as,  for  example,  Jupiter  with  his  four  satellites, 
or  Saturn  with  his  ring  and  seven.  Yet  to  so  high  a  de- 
gree of  perfection  has  modern  astronomy  advanced,  that 
Herschel  asserts  "  that  there  is  not  a  perturbation,  great 

What  is  meant  by  the  precession  of  equinoxes  ?  In  what  time  do  the 
equinoxial  points  make  one  revolution?  From  what  does  this  motion 
arise?  In  what  direction  does  the  earth's  axis  consequently  move?  Do 
any  known  perturbations  affect  the  validity  of  Newton's  theory  ? 


MEASUREMENT    OF    TIME.  373 

or  small  which  observation  has  ever  detected  which  has 
not  been  traced  up  to  its  origin  in  the  mutual  gravitation 
of  the  parts  of  our  system,  and  been  minutely  accounted 
for  in  numerical  amount  and  value  by  strict  calculation  on 
Newton's  principles  !"•  And  of  late  we  have  witnessed 
one  of  the  most  brilliant  results  of  modern  astronomy  in 
the  discovery  of  the  planet  Neptune.  For  it  was  seen 
that  Uranus  exhibited  disturbances  in  his  motions  not  ac- 
counted for  by  the  action  of  any  known  body.  These 
evidently  pointed  to  the  existence  of  some  other  mass  be- 
yond him,  which,  though  unseen,  was  exerting  its  in- 
fluence. The  magnitude  of  this  body  and  the  position  it 
should  occupy  were  determined  by  the  calculus ;  and, 
on  examining  the  region  of  the  heavens  designated,  the 
planet  was  found. 


LECTURE    LXXIII. 

OF  THE  MEASUREMENT  OF  TIME. — Sidereal  Day. — Solar 
Day. — Sidereal  Year. — Equation  of  Time. — Mean  and 
Apparent  Time. — Incommensurability  of  the  Day  and 
Year. —  The  Julian  Calendar. —  The  Gregorian  Calen- 
dar.—  Conclusion. 

IF  we  examine,  by  proper  instruments,  the  time  which 
elapses  between  the  successive  passages  of  any  star  what- 
ever over  the  meridian,  we  shall  find  that  it  is  uniformly 
23  hours,  56  minutes,  4  seconds.  It  is  immaterial  what 
star  is  watched  ;  all  give  the  same  result.  To  this  period 
the  name  of  a  sidereal  day  is  given. 

But  if,  with  the  same  instruments,  we  examine  the  me- 
ridian passages  of  the  sun  we  find  that  he  does  not  come 
upon  the  meridian  until  3  minutes  and  56  seconds  later 
each  day,  the  clock  measuring  24  hours  between  each 
passage.  To  this  period  the  name  of  a  solar  day  is  given. 

Now,  the  apparent  revolution  of  the  celestial  bodies  is 
due  to  the  actual  rotation  of  _the  earth  on  her  axis.  It 
\vould  seem  that  the  sun  and  the  stars  ought  all  to  ac- 
complish that  apparent  revolution  in  the  same  space  of 

What  is  meant  by  a  sidereal  day'?  What  is  its  length?  What  by  a 
solar  day  ?  What  is  its  length  ?  What  do  we  infer  as  respects  the  appa- 
rent motion  of  the  sun  ? 


374  MEAN    AND    APPAREIVT    TIME. 

time.  It  is,  therefore,  obvious  that  the  sun  must  move 
every  24  hours  about  one  degree  to  the  east :  such  a  mo- 
tion accounts  for  his  coming  later  on  the  meridian ;  for 
one  degree  is  passed  over  in  about  four  minutes  of  time, 
which  is  very  nearly  the  period  of  retardation  we  have 
observed.  In  90  days  the  sun  comes  on  the  meridian 
six  hours  later  than  the  star  with  which  he  was  first  com- 
pared. In  about  180  days  he  is  12  hours  later.  In  a  lit- 
tle more  than  365  both  come  on  the  meridian  together 
again.  But  this  apparent  easterly  motion  of  the  sun  is 
in  reality  the  orbitual  motion  of  the  earth  in  the  opposite 
direction,  arid  the  solar  day  differs  from  the  sidereal  by 
reason  of  the  revolution  of  the  earth  round  the  sun.  If 
that  revolution  did  not  take  place,  and  the  earth  only 
turned  on  her  axis,  the  solar  and  sidereal  days  would  be 
exactly  of  the  same  length  ;  but  that  revolution  existing, 
to  bring  the  sun  upon  the  meridian,  the  earth  must  make 
a  little  more  than  one  revolution  each  day,  and,  at  the 
end  of  365  days,  must  turn  on  her  axis  366  times — that 
is  to  say,  in  a  year  there  is  one  more  sidereal  than  there 
are  solar  days.  The  actual  length  of  the  sidereal  yearis 
366  days,  6  hours,  9  minutes,  12  seconds. 

These  considerations  show  how  the  measurement  of 
time  becomes  complicated  by  the  annual  motion  of  the 
earth  round  the  sun  ;  and,  as  the  axis  of  the  earth  is  in- 
clined to  her  orbit,  and  she  moves  with  different  degrees 
of  velocity  in  different  parts  of  her  elliptic  path,  more 
swiftly  as  she  approaches  the  sun  and  more  slowly  as  she 
recedes,  the  length  of  the  days  will  vary  from  time  to 
time,  when  compared  with  a  clock  that  goes  truly,  giving 
rise  to  a  difference  between  the  time  indicated  by  the 
sun  and  a  clock — a  difference  which  is  called  the  equa- 
tion of  time.  Mean  time  is  that  indicated  by  the  clock, 
and  apparent  time  that  indicated  by  the  sun. 

From  the  inclination  of  the  earth's  axis  to  the  ecliptic 
it  comes  to  pass  that  about  the  20th  of  March,  the  21st 
of  June,  the  23d  of  September,  and  the  21st  of  Decem- 
ber the  sun  and  the  clock  would  agree ;  but  between 
March  and  June  the  sun  is  faster  than  the  clock ;  from 
then  until  September  it  is  slower,  and  so  on.  The  differ- 
How  does  his  meridian  passage  compare  with  that  of  any  given  star? 
What  is  the  length  of  the  sidereal  day  ?  To  what  is  this  difference  due  ? 
What  is  equation  of  time?  What  is  mean  time  ?  What  is  apparent  tirrvo  ? 


THE    JULIAN    CALENDAR.  375 

ent  velocity  with  which  the  earth  moves  in  her  orbit  com- 
plicates this,  and  from  the  two  causes  together  the  coin- 
cidence takes  place  on  other  days — on  the  15th  of  April, 
the  15th  of  June,  the  31st  of  August,  and  the  24th  of  De- 
cember, while  the  greatest  difference  between  the  sun 
and  clock,  amounting  to  16  £  minutes,  takes  place  on  the 
1st  of  November. 

The  principal  natural  division  of  time  is  into  days  and 
years — a  division  which  is  based  upon  civil  wants,  and 
which,' therefore,  from  the  earliest  period  was  adopted. 
At  a  very  remote  time  it  was  discovered  that  the  year  con- 
tained about  365  days;  and  this  was  probably  the  first 
exact  division ;  but  after  a  while  it  was  discovered  that 
the  two  periods  are  in  reality  incommensurable,  and  that 
there  are  more  than  365  and  less  than  366  days  in  a  year. 
The  tropical  year,  as  we  have  already  stated,  consists  of 
865  days,  5  hours,  48  minutes,  49  seconds. 

The  first  great  historic  change  in  the  calendar  was 
made  by  Julius  Caesar,  who,  having  learned  in  Egypt,  that 
the  year  really  consisted  of  365  days  and  6  hours  nearly, 
endeavored  to  include  these  6  hours  by  adding  one  day  to 
each  fourth  year.  So  he  instituted  three  years  of  365  days, 
and  a  fourth  of  366.  The  latter  was  called  Bissextile. 
The  twelve  months  consisted,  some  of  thirty  and  s^me  of 
thirty-one  days,  but  February  had  only  twenty-eight  in 
common  years,  and  to  it  twenty-nine  were  given  in  bissex- 
tile. This  is  the  Julian  calendar-. 

It  is  evident,  however,  that  Julius  Caesar  had  thus  over- 
compensated  the  year.  It  does  not  consist  of  365  days 
and  6  hours,  but  wants  11  minutes  and  11  seconds  of  it. 
For  a  short  period  this  small  quantity  may  be  neglected, 
but  in  the  course  of  centuries  it  becomes  very  appreciable. 
In  the  year  1582  it  had  amounted  to  more  than  ten  days. 
At  this  time  Pope  Gregory  XIII. published  a  bull  requir- 
ing that  ten  days  should  be  cut  oft  from  that  year,  and  the 
fifth  of  October  be  reckoned  as  the  fifteenth,  and  by  a  most 
ingenious  and  simple  contrivance,  provided  against  the 
future  recurrence  of  the  difficulty.  The  years  are  to  be 

"On  what  days  do  the  sun  and  the  clock  agree?  When  is  there  the 
greatest  difference  ?  What  is  the  principal  division  of  time  ?  Are  the  day 
and  the  year  commensurable  ?  What  is  the  length  of  the  tropical  year? 
What  is  the  Julian  calendar  ?  In  what  was  it  defective  ?  What  was  the 
excess  of  compensation  ? 


376  THE  GREGORIAN  CALENDAR. 

enumerated  by  the  vulgar  chronology  of  the  birth  of 
Christ,  and  each  year,  the  number  of  which  is  not  divisi- 
ble by  4,  is  to  consist  of  365  days ;  but  every  year  which 
is  divisible  by  4  must  have  366,  except  it  be  also  divisible 
by  100.  Every  year  which  is  divisible  by  100,  but  not 
by  400,  has  365,  and  every  year  divisible  by  400  has  366. 

The  result  of  this  is,  that  in  400  years  three  bissextiles 
are  cut  off.  The  year  1600  was  bissextile  ;  1700,  1800, 
and  1900  are  not ;  but  the  year  2000  will  be,  and  so  per- 
fect is  this  contrivance  that  the  derangement  will  be  less 
than  one  day  in  the  course  of  3000  years.  Even  this 
might  be  avoided  if  the  years  divisible  by  4000  should 
be  made  to  consist  of  365  days,  and  then,  in  the  course  of 
one  hundred  thousand  years,  the  derangement  of  the  cal- 
endar would  not  amount  to  a  single  day.  This  is  the 
Gregorian  calendar,  or  new  style.  It  is  received  now  in 
all  Christian  countries,  save  those  in  which  the  mode  of 
faith  is  according  to  the  Greek  church — their  years  and 
festivals  occur  twelve  days  later  than  ours. 

It  is  scarcely  necessary  to  add  the  subsidiary  division 
of  time  : — The  week,  consisting  of  seven  days — a  prime- 
val division,  which  is  to  be  traced  in  all  countries,  and 
which  has  survived  all  legislative  enactments  and  changes 
of  empires,  because  it  is  suitable  to  the  wants,  and  com- 
mends itself,  with  its  seventh  day  of  rest,  to  the  well-be- 
ing of  man  ;  the  month,  which  consists  of  four  weeks  ; 
and  the  seasons,  of  which  there  are  four  in  each  year-^ 
spring,  summer,  autumn,  and  winter.  The  names  of  the 
seven  days  of  the  week  are  derived  from  those  of  the  sun, 
moon,  and  planets — an  observation  which  holds  even  for 
modern  languages.  These  names  were  imposed  by  pious 
men  at  a  very  remote  period  ;  for  they,  having  remarked 
the  geometrical  beauty  of  the  revolutions  of  the  stars,  and 
the  amazing  punctuality  with  which  they  complete  their 
periodic  motions,  were  led  to  suppose  that  they  were 
guided  by,  or  rather  were  the  residences  of  intellectual 
principles.  They  little  foresaw  how  the  great  discovery 
of  Newton — universal,  gravitation — would  remove  the  hy- 
pothetical beings  they  thus  worshipped,  from,  the  domains 

By  whom  and  when  was  this  corrected?  How  did  he  adjust  the  calen- 
dar? To  what  degree  of  perfection  does  this  division  reach  ?  What  is 
New  Style?  In  what  countries  is  it  not  adopted  ?  What  other  popular 
divisions  of  time  have  we  ?  From  what  are  the  names  of  the  days  derived  ? 


CONCLUSION.  377 

of  the  solar  system,  and  replace  them  by  one  far-reach- 
ing mechanical  principle — a  principle  so  enduring,  so  un- 
changeable, that  relying  on  it  the  astronomer  is  able  to 
look  equally  into  the  past  and. the  future,  reproducing  an- 
cient events,  or  predicting  those  that  are  to  take  place  in 
coming  centuries;  and  this  not  in  a  doubtful  or  shadowy 
manner,  but  with  all  the  precision  of  time,  place,  and  cir- 
cumstance. And  this  is  the  uniform  course  of  human, 
knowledge  :  things  which  are  imputed  by  one  generation 
to  special  and  incessant  interpositions  of  divine  agents, 
are  discovered  by  another  to  be  the  direct  results  of  eter- 
nal and  uniform  laws ;  and  the  Universe,  far  from  owing 
its  permanence  and  regularity  to  the  cares  of  a  thousand 
gods  and  goddesses,  contains  within  itself  its  own  princi* 
pies  of  conservation — all  its  perturbations  run  through 
their  particular  cycles,  and  then  they  compensate  them- 
selves, and  every  thing  returns  to  its  pristine  condition. 
It  contains  no  element  of  destruction,  nor  even  of  decay, 
and  could,  under  the  simple  laws  impressed  upon  it,  con- 
tinue its  existence  through  all  eternity,  except  its  Al- 
mighty Maker — a  monument  of  whose  power  and  wisdom 
it  is — should  see  fit  to  interfere. 


INDEX. 


Aberration  of  light,  177. 
stars,  367. 

Accidental  colors,  231. 
Achromatic  lens,  203. 
Acoustics,  157. 
Acoustic  figures,  169. 
Action  and  reaction,  79. 
Air-pump,  17. 
Annual  parallax,  349. 
Anomaly,  354. 
Archimedes's  screw,  65. 
Areometers,  53. 
Artesian  wells,  59. 
Asteroids,  334. 
Astronomy,  315. 
Atmosphere,  12. 

color  of,  13. 

height  of,  13. 
A tt wood's  machine,  87., 
Aurora  borealis,  287. 

B. 

Balance,  129. 
Ballistic  pendulum,  94. 
Bali-cock,  68. 
Balloon,  37. 
Barometer,  24. 
Beaume's  hydrometer,  54. 
Bellows,  hydrostatic,  48. 
Boiler,  270. 

Bohnenberger's  machine,  80. 
Boyle's  law,  31. 
Bramah's  press,  49. 
Breast-wheel,  63. 
Burning- lens,  195. 

C. 

Camera  obscura,  232. 
Capacity  for  heat,  258. 
Capillary  attraction,  101. 
Cartesian  images,  29. 
Center  of  gravity,  110. 
Chromatic  aberration,  202. 
Colors,  200. 
Comets,  338. 
Composition  of  forces,  73. 


Compound  motion,  72. 
Compressibility  of  air,  14. 
Condenser,  29. 
Contracted  vein,  61. 
Conduction  of  heat,  253. 
Cords,  vibrations  of,  163. 
Currents  in  air,  37. 
Cycloid,  118. 


Daniel's  hygrometer,  276. 
Decomposition  of  water,  300. 
Differential  thermometer,  247 
Diffraction,  209. 
Diiftision,  39. 
Direction  of  motion,  70. 
Dispersion  of  light,  196. 
Distinctive  properties,  2. 
Diving-bell,  6. 
Divisibility,  8. 

E. 

Earth,  figure  of,  364. 
Echoes,  166. 
Eclipses,  343.  f 

Elastic  impact,  122. 
Elasticity,  7. 

of  air,  15,28. 
Electricity,  288. 
Electro-dynamic  helix,  308. 
•Electrometer,  297. 
Slectro-magnetism,  304. 
Ulectrotype,  303. 
Cndosmosis,  105. 
Exchanges  of  heat,  251. 
Expansion,  257. 
Evaporation,  262. 
xtension,  2. 

F. 

'ailing  bodies,  85. 
ixed  lines,  199. 
'loating  bodies,  67. 
•'lorentine  experiment,  43. 
"lowing  of  liquids,  60. 
>rces,  9. 

composition  of,  73. 


380 


INDEX. 


Forcing-pump,  64. 
Forms  of  bodies,  1. 
Fountain  in  vacuo,  27. 
Fountains  by  pressure,  57. 
Friction,  142. 

G. 

Gases,  specific  gravity  of,  52. 
Gravity,  70. 
Gravitation,  80. 
Gravimeter,  54. 
Gregorian  calendar,  376. 

H. 

Heat,  properties  of,  244. 
Heights,  determination  of,  25. 
Hydraulic  press,  49. 
Hydro-dynamics,  45. 
Hygrometry,  272. 


Impenetrability,  3. 
Inclined  plane,  137. 

motion  on,  90. 
Induction,  293. 
Inequalities,  370. 
Inertia,  77. 
Interference,  154. 

J. 

Julian  calendar,  375. 
Jupiter,  334. 

K. 

Kepler's  laws,  355. 


Latent  heat,  260. 

Latitude,  368. 

Lenses,  190. 

Level  of  liquids,  46. 

Lever,  127. 

Leyden  jar,  294. 

Light,  properties  of,  168. 

theories  of,  205. 

velocity  of,  176. 
Liquids,  properties  of,  41. 
pressures  of,  56. 
Longitude,  368. 

M. 

Machines,  electrical,  290. 
Magdeburg  hemispheres,  22. 
Magic  lantern,  236. 
Magnetism,  278. 

terrestrial,  283. 


Magneto-electricity,  309. 
Marriotte's  law,  31. 
Mars,  333. 

Mechanical  powers,  126. 
Mercurial  pendulum,  120. 
Mercury,  329. 
Microscope,  233. 
Mirage,  226. 
Momentum,  78. 
Monochord,  162. 
Moon,  340. 

Montgolfier's  balloon,  37. 
Motion,  69. 

Motion  round  a  center,  94. 
Multiplier,  305. 
Multiplying-glass,  189. 

N. 

Nebulae,  351. 
Neptune,  337. 
Newton's  laws,  80. 
rings,  208. 

O. 

Occultation,  345. 
Oersted's  machine,  44. 
Overshot-wheel,  62. 

P. 

Parachute,  33. 
Paradox,  hydrostatic,  48. 
Parallax,  323. 
Passive  forces,  141. 
Pendulum,  116. 
Percussion,  121. 
Perturbations,  369. 
Photometry,  172. 
Planetary  motions,  97. 
Plumb-line,  84. 
Pneumatic  trough,  23. 
Point  of  application,  70. 
Polarization,  210. 
Precession  of  equinox,  372. 
Pressure  of  air,  21. 

hydrostatic,  47. 

of  liquids,  56. 
Prism,  188. 
Projectiles,  92. 
Psychrometer,  277. 
Pulley,  131. 
Pump,  63. 

R. 

Radiant  heat,  249. 
Radius  vector,  98. 
Rainbow,  221. 


INDEX. 


381 


Refraction,  184. 
Refraction,  double,  21 5. 

of  heat,  252. 

atmospheric,  223. 
Reflexion,  178. 
Resistance  of  air,  32. 

of  media,  143. 
Resolution  of  forces,  75. 
Rest,  69. 
Rigidity  of  cordage,  145. 

S. 

Sap,  rise  of,  106. 

Saturn,  335.          , 

Saussure's  hygrometer,  275. 

Screw,  139. 

Sea',  41. 

Seasons,  326. 

Shadows,  171. 

Solar  micrdscope,  237. 

system,  337. 
Soniferous  media,  159. 
Sound,  157. 

conducted,  34,  158. 
Specific  gravity,  50. 
Specific  heat,  260. 
Spectacles,  230. 
Spherometer,  5.  . 
Spouting  of  liquids,  61. 
Stability  of  bodies,  113. 
Stars,  fixed,  346. 
Steam  engine,  267. 
Stream-measurer,  62. 
Strength,  108. 
Sun,  324. 
Syphon,  66. 
Syringe,  18. 


T. 

Telegraph,  magnetic,  312. 
Telescope,  238. 
Thermo-electricity,  313. 
Thermometer,  245. 
Thousand-grain  bottle,  51. 
Tides,  358. 
Time,  373. 
Torsion  balance,  109. 
Transits,  332. 
Trumpet,  hearing,  167. 

speaking,  166. 
Twilight,  225. 


Unchangeability,  4. 
Undershot-wheel,  62. 
Undulations,  14T. 
Undulatory  theory,  205. 
Uranus,  336. 

V. 

Vapors,  265. 
Venus,  329. 
Vera's  pump,  65. 
Vibrations,  148. 
Virtual  velocities,  127. 
Voltaic  battery,  298. 

W. 

Water,  compressibility  of,  44. 
Wedge,  138. 
Weight  of  air,  19. 
Wheel  and  axle,  134. 
Windlass,  135. 

Z. 

Zaniboni's  piles,  296. 


THE   END. 


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Classical  Dictionary, 

Containing  an  Account  of  the  principal  Proper  Names  mentioned  in 
Ancient  Authors,  and  intended  to  elucidate  all  the  important 
Points  connected  with  the  Geography,  History,  Biography,  My- 
thology, and  Fine  Arts  of  the  Greeks  and  Romans,  together  with 
an  Account  of  the  Coins,  Weights,  and  Measures  of  the  Ancients, 
with  Tabular  Values  of  the  same.  Royal  8vo,  Sheep  extra.  §4  75. 

The  scope  of  this  great  work  is  very  extensive,  and  comprises  information  respect- 
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a  complete  encyclopedia  of  Ancient  Geography,  History,  Biography,  and  Mythology 
The  department  of  the  Fine  Arts  forms  an  entirely  new  feature  ;  embracing  biogra- 
phies of  ancient  artists,  and  criticisms  upon  their  productions.  In  fine,  this  noble 
work  is  not  only  indispensable  to  the  classical  teacher  and  student,  but  eminently 
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aims  to  be  complete.  It  has  been  pronounced  by  Professor  Boeckh  of  Berlin,  one  of 
the  leading  scholars  in  Germany,  "  a  most  excellent  work." 

Slutftou's  Hatttt  Urssons. 

Latin  Grammar,  Part  I.  Containing  the  most  important  Parts  of 
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each  step  of  his  progress,  with  those  portions  of  the  grammar  which  he  may  from  time 
to  time  commit  to  memory,  and  which  relate  principally  to  the  declension  of  noun* 
and  conjugation  of  verbs.  As  soon  as  the  beginner  has  mastered  some  principle  rel- 
ative to  the  inflections  of  the  language,  his  attention  is  directed  to  exercises  in  trans- 
lating and  writing  Latin,  which  call  for  a  practical  application  of  the  knowledge  he 
may  have  thus  far  acquired ;  and  in  this  way  he  is  led  on  by  easy  stages,  until  he  is 
made  thoroughly  acquainted  with  all  th«  important  rule*  that  regulate  the  inflection* 
of  the  Latin  tongu«. 


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&nthon'0  SlatCn  J^rose  Composition. 

Latin  Grammar,  Part  II.  An  Introduction  to  Latin  Prose  Composi- 
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plan  pursued  is  (.he  same  with  that  which  was  followed  in  preparing'  the  first  part, 
and  the  utility  of  which  has  been  so  fully  proved  by  the  favorable  reception  extended 
to  that  volume.  A  rule  is  laid  down  and  principles  are  stated,  and  then  exercise* 
are  given  illustrative  of  the  same.  These  two  parts,  therefore,  will  form  a  Grammar 
of  the  Latin  Language,  possessing  this  decided  advantage  over  other  grammars,  ia 
its  containing  a  Complete  Course  of  Exercises,  which  have  a  direct  bearing  on  each 
step  of  the  student's  progress. 

&nthon'j9  HCctfonarg  of  (ffireeit  an*  Itoman 
atnttquftfe*, 

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of  the  most  eminent  German  Philologists  and  Jurists.  Edited  by 
WILLIAM  SMITH,  Pn.D.  Illustrated  by  a  large  number  of  Engrav- 
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5»^ 
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young  student,  and,  as  a  book  of  reference,  will  be  most  acceptable  on  the  library  ta- 


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It  forms  the  fourth  and  concluding  part  of  the  Latin  Lessons 


WORKS    FOR    COLLEGES    AND    DISTRICT    SCHOOLS.         3 

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the  finest  scholars  in  the  country. 

atntfum'*  SStorfts  of  fgorace, 

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&ntfum'0  jFCrat  <!£reelt  actons, 

Containing  the  most  important  Parts  of  the  Grammar*of  the  Greek 
Language,  together  with  appropriate  Exercises  in  the  translating 
and  writing  of  Greek,  for  the  Use  of  Beginners.  12mo,  Sheep 
extra.  90  cents. 

The  plan  of  this  work  is  very  simple.  It  is  intended  to  render  the  study  of  the 
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to  produce  an  abiding  impression.  With  this  view,  there  is  appended  to  the  several 
divisions  of  the  Grammar  a  collection  of  exercises,  consisting  of  short  sentences,  in 
•which  the  rules  of  inflection  just  laid  down  are  fully  exemplified,  and  which  the  stu- 
dent is  required  to  translate  and  parse,  or  else  to  convert  from  ungrammatical  to  gram- 
matical Greek. 


(Eonrjiositton. 

Greek  Lessons,  Part  II.  An  Introduction  to  Greek  Prose  Composi- 
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ordinary  grammar  with  all  the  important  principles  of  the  Greek  Syntax.  And  in 
order  to  impress  these  principles  more  fully  upon  the  mind  of  the  pupil,  they  are  ac- 
companied by  exercises  explanatory  of  the  same  ;  in  other  words,  the  theory  is  first 
given,  and  its  practical  application  follows  immediately  after.  This  is  the  only  mode 
of  familiari2ing  the  student  with  the  niceties  of  Greek  construction,  and  has  never 
been  carried  out  to  so  full  an  extent  in  any  similar  work. 


CKrammar  of  tfie  <£reefc  Slanguage, 

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•swhole  continuance.  Nothing  has,  therefore,  been  omitted  the  want  of  which  might  in 
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Every  effort  has  been  made  to  exhibit  a  concise  outline  of  all  the  leading  principles 
of  Greek  philology. 


WORKS    FOR    COLLEGES    AND    DISTRICT    SCHOOLS.         5 

&nt!vott>s  3£efc  <£mfc  Grammar 

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those  of  Kiihiier,  which  are  now  justly  regarded  as  the  ablest  of  their  kind  ;  and  the 
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&nthotf  is  ©rcrft  llrosottg  airtr  S&etre, 

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is  useful  to  the  young  student  in  furthering  his  acquaintance  with  the  classic  language 
and  noble  poetry  of  Homer.  The  Glossary  renders  any  other  Homeric  dictionary 
useless. 


Principally  from  the  German  of  Jacobs.  With  English  Notes,  crit- 
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of  Xcuojrtion, 

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WORKS    FOR    COLLEGES    AND    DISTRICT    SCHOOLS. 


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antt  (Eroo&s's  jFtrst  Uooft  Cn 


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flattn, 

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may  thus  either  extend  a  taste  for  such  studies,  or  tend  to  satisfy  the  taste  already 
widely  diffused,  can  not  but  be  hailed  with  pleasure  by  all  who  feel  an  interest  in  the 
progress  of  general  science,  and  especially  by  those  who,  with  me,  recognize  the  pre- 
eminently practical  character  of  that  knowledge  which  pertains  to  the  human  mind. 
—Prof.  CALDWELL,  Dickinson  College. 


WORKS    FOR    COLLEGES    AND    DISTRICT    SCHOOLS.         7 

Elements  oe  JEteutal 


Embracing  the  two  Departments  of  the  Intellect  and  the  Sensibili- 
ties.    2  vols.  12mo,  Sheep  extra.     $2  50. 

An.  Abridgment  of  the  above,  by  the  Author,  designed  as  a  Text-book  in  Acad- 

emies.    12uio,  Sheep  extra.    $1  25. 

Professor  Upham  has  brought  together  the  leading-  views  of  the  best  writers  on  the 
most  important  topics  of  mental  science,  aud  exhibited  them  with  great  good  judg- 
ment, candor,  clearness,  and  method.  Out  of  all  the  systematic  treatises  in  use,  we 
consider  the  volumes  of  Mr.  Upham  by  far  the  best  that  we  have.  —  New  York  Review 

^Treatise  on  tfce  SirciL 

A  Philosophical  and  Practical  Treatise  on  the  Will.     12mo,  Sheep 
extra.     $1  25. 

This  work  is  one  of  great  value  to  the  literary  and  religious  community.  It  indi- 
cates throughout  not  only  deep  and  varied  research,  but  profound  and  laborious 
thought,  and  is  a  full,  lucid,  and'  able  discussion  of  an  involved  and  embarrassing  sub- 
ject. The  style,  though  generally  diffuse,  is  always  perspicuous,  and  often  elegant  ; 
and  the  work,  aia  whole,  will  add  much  to  the  reputation  of  its  author,  and  entitle 
him  to  rank  among  the  ablest  metaphysicians  of  our  country.—  Christian  Advocate. 


Btcttonarg; 

A  Vocabulary  of  the  Technical  Terms  recently  introduced  into  Ag- 
riculture and  Horticulture  from  various  Sciences,  and  also  a  Com- 
pendium of  Practical  Farming  :  the  latter  chiefly  from  the  Works 
of  the  Rev.  W.  L.  RHAM,  LOUDON,  Low,  and  YOUATT,  and  the 
most  eminent  American  Authors.  With  numerous  Illustrations. 
12mo,  Sheep  extra,  81  75  ;  Muslin  gilt,  $1  50. 

An  invaluable  treatise  for  the  agriculturist,  whose  suggestions  and  information 
would  probably  save  him  ten  times  its  cost  every  year  of  his  labor.  —  Evangelist. 

In  the  Farmer's  Dictionary  we  find  what  has  never  before  been  drawn  up  for  the 
farmer  :  no  where  else  is  so  much  important  information  on  subjects  of  interest  to  the 
practical  agriculturist  to  be  found.  —  Cultivator. 

iJuers  ^Farmer's  (fcomjjanton; 

Or,  Essays  on  the  Principles  and  Practice  of  American  Husbandry. 
With  the  Address  prepared  to  be  delivered  before  the  Agricultural 
and  Horticultural  Societies  of  New  Haven  County,  Connecticut. 
And  an  Appendix,  containing  Tables,  and  other  Matter  useful  to 
the  Farmer.  To  which  is  prefixed  a  Eulogy  on  the  Life  and 
Character  of  Judge  BUEL,  by  AMOS  DEAN,  Esq.  12mo,  Muslin. 
75  cents. 

"  This  is  decidedly  one  of  the  best  elementary  treatises  on  agriculture  that  has 
ever  been  written.  It  contains  a  lucid  description  of  every  branch  of  the  subject, 
and  is  in  itself  a  complete  manual  of  Husbandry,  which  no  farmer,  who  would  un- 
derstand his  own  interest,  should  be  without.  It  is  sufficient  to  say  that  this  is  the 
last  production  of  the  late  Judge  Buel,  and  contains  his  matured  experience  and  opin- 
ions on  a  subject  which  he  did  more,  perhaps,  to  elevate  and  promote  than  any  other 
man  of  his  time.  Judge  Buel  was  a  strong  advocate  for  what  is  termed  the  New 
Husbandry,  the  many  advantages  of  which  over  the  old  system  he  illustrated  by  his 
own  practice,  and  the  claims  of  which  to  the  consideration  of  the  farmer  are  ably  set 
forth  in  this  volume.  The  work  is  written  with  great  perspicuity,  and  the  manner 
in  which  the  subject  is  treated  shows  the  hand  of  a  master.  The  clearness  and  sim- 
plicity of  the  style  adapt  it  to  all  classes  of  readers  ;  and  containing  as  it  does  a  co- 
pious Index,  Glossary,  <fec.,  it  is  eminently  suited  as  a  text-book  for  country  schools, 
into  which  we  hope  it  will  be  speedily  introduced,  and  its  principles  thoroughly  studied 
and  practically  carried  out.  It  is  also  a  very  suitable  book  to  be  given  as  a  premium, 
and  we  therefore  recommend  it  to  the  notice  of  our  Agricultural  Societies." 


8         WORKS    FOR    COLLEGES    AND    DISTRICT   SCHOOLS. 

STejrNboofc  of 


For  the  Use  of  Schools  and  Colleges.  With  nearly  300  Illustrations. 
12mo,  Sheep.  75  cents.  (Third  Edition,  revised.) 

Terse,  lucid,  and  philosophical,  and  well  adapted  to  the  object  for  which  it  is  pub- 
lished. It  is  a  vast  improvement  upon  all  the  chemical  text-books  with  which  we-are 
acquainted.  It  can  not  fail  of  superseding  the  many  compends  now  used  in  our  col- 
i>g*.s.— St.  Louis  Gazette. 

(EftemCcal  ©r0anf?atioH  of  plants. 

A  Treatise  on  the  Forces  which  produce  the  Organization  of  Plants. 
With  an  Appendix,  containing  several  Memoirs  on  Capillary  At- 
traction, Electricity,  and  the  Chemical  Action  of  Light.  En- 
gravings. 4to.  $2  50. 

Dr.  Draper's  researches  in  the  Chemistry  of  Plants  and  on  the  Chemical  Action  of 
Mght  here  given,  render  this  work  exceedingly  valuable  to  all  lovers  of  science.  The 
tuthor  is  well  known  as  a  most  able  and  indefatigable  experimenter  and  theorist  in 
philosophy. — Commercial  Advertiser. 

STe):t^boofc  of  Jlatnral 

For  the  Use  of  Schools  and  Colleges.  With  numerous  Illustrations 
12mo.  (In  press.) 

J&gstem  of 

For  the  Use  of  Schools.  Illustrated  by  more  than  50  Cerographio 
Maps,  and  numerous  Engravings  on  Wood.  4to.  50  cents. 

A  valuable  acquisition  to  all  engaged  either  in  imparting  or  receiving  instruction 
Its  conciseness  and  simplicity  of  arrangement,  and  its  numerous  and  beautiful  em- 
bellishments, can  not  fail  to  render  it  deservedly  popular. — W.  H.  PILE,  Principa 
of  N.  E.  Grammar  School,  Philadelphia. 

The  Public  School  Society  of  the  city  of  New  York  have  unanimously  adopted 
Morse's  School  Geography  into  their  extensive  schools,  and  it  has  been  generally  in- 
troduced into  those  of  Philadelphia. 

(£erofiraj)!itc  J&ajm, 

Comprising  the  whole  Field  of  Ancient  and  Modern,  including  Sa- 
cred Geography,  Chronology,  and  History.  Publishing  in  Num- 
bers, folio  size,  each  containing  four  colored  Maps,  executed  from 
the  latest  improved  authorities.  The  first  9  Numbers  form  a 
complete  American  Atlas.  Price  25  cents  each  Number. 

This  much-needed  atlas  will  be  welcomed  by  ail  engaged  in  teaching  in  colleges, 
schools,  &c.  ;  it  is  an  admirable  help  in  ge~braphical  studies;  and  thousands  who  are 
constantly  requiring  the  help  of  a  competent  and  reliable  atlas  will  find  this  just  to 
their  purpose,  and  excessively  cheap  in  the  bargain  It  will  form,  when  completed 
the  most  complete  universal  atlas  extant. 

J&entotcft's  JFtrst  iprtncfjjies  of  (EJicmtetrg ; 

Being  a  familiar  Introduction  to  the  Study  of  that  Science.  Wit,, 
Questions.  Engravings.  18mo,  half  Sheep.  75  cents. 

The  principle  by  which  the  author  has  been  governed  was  to  admit  few,  if  any, 
hard  terms  in  the  text,  supplying  their  place  with  as  plain  language  and  intelligible 
explanations  as  possible.  In  a  word,  more  information  or  instruction  will  be  found 
in  this  little  work  than  can  be  collected  from  many  publications  of  greater  pretensions 
and  of  four  times  its  bulk 


WORKS    FOR    COLLEGES    AND    DISTRICT    SCHOOLS.         i) 

Jftrntofcfe's  practical  J&ecfiatucs. 

Applications  of  the  Science  of  Mechanics  to  Practical  Purposes. 
Engravings.     18mo,  half  Sheep.     90  cents. 

This  volume  is  alike  creditable  to  the  writer,  and  to  the  state  of  science  in  this 
country.  —  American  Quarterly  Review. 

a  JFirst  principles  of  Natural 


Being  a  familiar  Introduction  to  the  study  of  that  Science.  With 
Questions.  Engravings.  18mo,  half  Sheep.  75  cents. 

This  work  contains  treatises  on  the  sciences  of  statics  and  hydrostatics,  comprising 
the  whole  theory  of  equilibrium.  It  is  intended  for  the  use  of  those  who  have  no 
knowledge  of  mathematics,  or  who  have  made  hut  little  progress  in  their  mathemat- 
ical reading.  Throughont  the  whole,  an  attempt  has  been  made  to  bring  the  princi- 
ples of  exact  science  to  bear  upon  questions  of  practical  application  in  the  arts,  and 
to  place  the  discussion  of  them  withm  the  reach  of  those  connected  -with  manufac- 
tures. 

Potter's  Political  Saconoms  : 

Its  Objects,  Uses,  and  Principles  ;  considered  with  reference  to  the 
Condition  of  the  American  People.  With  a  Summary  for  the  Use 
of  Students.  18mo,  half  Sheep.  50  cents. 

Two  objects  have  been  kept  in  view  in  preparing  this  work:  first,  to  provide  a 
treatise  for  general  readers  adapted  to  the  times,  and  especially  to  the  wants  of  our 
country,  which  should  not.  be  encumbered  unnecessarily  with  controversial  mutters, 
or  with  abstract  discussions  ;  secondly,  to  furnish  a  cheap  and  convenient  manual  for 
seminaries,  in  which  larger  and  more  expensive  text-books  could  not  well  be  used." 

Parfeer's  &itrs  to  Snsltsli  Composition, 

Prepared  for  the  Student  of  all  Grades,  embracing  Specimens  and 
Examples  of  School  and  College  Exercises,  and  most  of  the  higher 
Departments  of  English  Composition,  both  in  Prose  and  Verse. 
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We  have  been  long  familiar  with  this  excellent  volume,  and  do  not  «on«eive  it  pos 
sible  for  any  improvement  to  be  made  on  it.  To  those  who  have  never  had  an  oppor- 
tunity of  judging  of  its  merits,  we  would  say,  by  all  means  procure  a  copy,  for  there 
is  nothing  like  it  in  the  whole  range  of  elementary  school-books.  —  Commercial  j)dv 


ideographical  (&ucstfons, 

Adapted  for  the  Use  of  Morse's,  Woodbridge's,  Worcester's,  Mitch- 
ell's, Field's,  Malte  Brun's,  Smith's,  Olney's,  Goodrich's,  or  any 
other  respectable  Collection  of  Maps"  embracing,  by  way  of 
Question  and  Answer,  such  Portions  of  the  Elements  of  Geogra- 
phy as  are  necessary  as  an  Introduction  to  the  Study  of  the  Maps. 
To  which  is  added,  a  concise  Description  of  the  Terrestrial  Globe 
12mo,  Muslin.  25  cents 

These  Questions  embrace  none  of  the  tedious  and  uninteresting  details  of  geogra- 
phy. They  are  designed  to  simplify  the  study  of  this  important  science,  by  means 
of  the  useful  and  important  process  of  classification.  There  are  few  questions  among 
them  that  can  not  be  answered  from  any  respectable  atlas  ;  and  the  author  trusts  that 
they  will  prove  useful  and  convenient  on  this  account,  as  they  may  be  used  without 
subjecting  a  class  of  pupils  to  the  expense  frequently  attendant  on  a  required  uniform- 
ity of  maps.  These  Questions  are  already  used  ia  some  of  the  leading  schools  in 
New  England. 


10      WORKS    FOR    COLLEGES    AND    DISTRICT    SCHOOLS. 


Or,  Elements  of  a  new  System  of  Mental  Philosophy,  on  the  Basis 
of  Consciousness  and  Common  Sense.  Designed  for  Colleges 
and  Academies.  12mo,  Muslin.  $1  00. 

This  production,  the  fruit  of  some  20  years'  scholastic  experience,  avowedly  owoa 
its  existence  to  the  desire  of  the  author  to  promote  the  cause  of  truth  and  science 
U  exhibits  in  a  lucid  manner  the  analysis  of  mental  philosophy  as  the  basis  of  meta- 
physical science  and  religious  belief. 

<3talfteWg  (Eomjjentttum  of  Homan  atrtr  <&ve= 
ctan  ^nttqutttcs, 

Including  a  Sketch  of  Ancient  Mythology.  With  Maps,  &c.  12mo, 
Muslin.  37i  cents. 

Most  of  the  works  in  use  which  treat  of  the  antiquities  of  Greece  and  Rome  are 
so  copious  and  so  intermingled  with  Greek  or  Latin  quotations,  that,  though  they  may 
be  highly  valuable  to  the  classical  scholar  as  works  of  reference,  they  are  rendered- 
less  useful  to  the  classical  pupil  as  common  text-books.  On  this  account,  the  study 
of  classical  antiquities  has  been  mostly  confined  to  the-  higher  classes.  The  present 
volume  is  designed  for  general  use  in  our  common  schools,  but  it  is  believed  to  be  so 
comprehensive  and  elevated  in  its  character,  as  to  be  acceptable  in  academies  and 
high  schools  as  well  as  private  use. 

Salfceltr's  jFtrst  3$oofc  tn  JSbpauteli; 

Or,  a  Practical  Introduction  to  the  Study  of  the  Spanish  Language. 
Adapted  to  every  Class  of  Learners,  containing  full  Instructions 
in  Pronunciation  ;  a  Grammar  ;  Reading  Lessons  and  a  Vocabu- 

%  lary.     (In  press.) 

I  have  never  met  with  a  work  professing  to  teach  any  foreign  language  which  com- 
bines so  many  excellent  qualities,  and  is  so  well  adapted  for  all  classes  of  learners. 
It  is  the  precise  manner  in  which  I  have  been  giving  instruction  to  classes  of  pupils 
in  English,  French,  and  Spanish  for  many  years  in  the  cities  of  Paris,  London,  and 
Madrid,  teaching  what  is  most  important  to  know.  —  Don  JULIO  CIRILO  DE  MOLINA, 
Professor  of  Languages  in  the  Cities  of  Madrid,  Paris,  and  London. 

i$ogtt'£  JBltmtntn  o£  2&Hetoric  autr  Uttrrarg 
(grtttctem, 

With  copious  Practical  Exercises  and  Examples.  Including,  also, 
a  Succinct  History  of  the  English  Language,  and  of  British  and 
American  Literature,  from  the  earliest  to  the  present  Times. 
On  the  Basis  of  the  recent  Works  of  Alexander  Reid  and  Robert 
Connell  ;  with  large  Additions  from  other  Sources.  Compiled 
and  arranged  by  J.  R.  BOYD,  A.M.  12mo,  half  Bound.  50  cents. 

It  is  very  happily  adapted  to  aid  teachers  in  training  the  minds  of  the  young  to  act 
with  clearness,  and  to  give  a  perspicuous  and  elegant  expression  to  their  thoughts  in 
written  language.  —  Philadelphia  Christian  Observer. 

My  decided  conviction  of  its  merits  prompts  me  to  recommend  it  to  the  examination 
of  teachers,  parents,  and  all  who  feel  an  interest  in  promoting  the  noble  and  blessed 
career  of  popular  education.  —  S.  N.  SWEET,  Author  of  "  Elocution." 

BogtTs  3Sclecttt  J*toral  Vhflosoirtig. 

Prepared  for  Literary  Institutions  and  General  Use.  12mo,  Muslin 
gilt.  75  cents. 

The  book  before  us  is  exceedingly  valuable,  both  for  private  uso  and  academies  and 
high  schools  generally.  Though  not  so  able  a  work  as  Wayland's  "  Moral  Science," 
"it  exhibits  in  detail  the  greater  and  the  lesser  moralities  of  life,"  and  is  therefore 
oetter  adapted  for  union  district  schools.  It  can  not  b«  studied  too  much,  by  youth 
especially.  —  Western  Literary  Messenger 


WORKS    FOR    COLLEGES    AND    DISTRICT   SCHOOLS.      11 

Jilautus's  "SThe 

A.  Comedy  of  Plautus.  With  English  Notes,  for  the  Use  of  Stu- 
dents. By  JOHN  PROUDFIT,  D.D.  18mo,  Muslin.  37$  cents. 

Plautus  possessed  very  happy  talents  for  a  comic  writer,  a  rich  flow  of  excellent 
wit,  happy  invention,  aiid  all  the  force  of  comic  expression. — Eschb. 

Jtorl  an*  fchapsars  3£cto  System  oe  JFrcncft 
(Grammar, 

Containing  the  First  Part  of  the  celebrated  Grammar  of  these  Au- 
thors. Arranged  with  Questions,  and  a  Key  in  English.  Also, 
an  Abridgment  of  the  Syntax  and  Grammatical  Analysis  of  the 
same  Authors.  To  which  are  added,  Lessons  in  Reading  and 
Speaking,  Forms  of  Drafts,  Advertisements,  &c.  Designed  to 
facilitate  the  Student  in  the  Use  of  the  French  Language,  1st.  By 
making  it  a  Medium  -of  Communication  between  himself  and 
Teacher.  2d.  By  enabling  him  to  read,  write,  and  speak  it  on  all 
Occasions.  By  SARAH  E.  SEAMAN.  Revised  and  corrected  by 
Professor  C.  P.  BORDENAVE.  12mo,  Muslin.  75  cents. 

The  Grammar  of  Nog!  and  Chapsal  is  universally  considered  to  be  the  best,  and  is 
the  one  most  generally  used  in  our  academies.  The  form  of  question  and  answer 
adopted  by  Mrs.  Seaman,  with  the  translated  key  at  the  end.  are  evident  improve- 
ments. I  do  not  hesitate  to  recommend  the  work. — C.  LE  FEBVRE. 

I  have  so  high  an  opinion  of  the  judgment  of  M.  Le  FebVre,  that  any  work  which 
meets  with  his  approbation  will  command  mine. — CHARLES  ANTHON. 

SBCU's  Xogfc,  &atfoctnatfte  airtr  Xirtmcttte; 

Being  a  connected  View  of  the  Principles  of  Evidence  and  Methods 
of  Scientific  Investigation.  8vo,  Muslin.  $2  00V 

A  production,  we  predict,  which  will  distinguish  the  age  ;  which  no  scholar  should 
be  without ;  but  which,  alxwe  all,  should  be  the  manual  of  every  lawyer.  The  style 
is,  in  our  judgment,  a  model  ;  in  thought  as  in  method,  clear  as  crystal ;  iu  expres 
won.  precise  as  the  symbolical  language  of  algebra. — Democratic  Review. 

JHaurg's  $rincf|)ic$  of  Sloqucnce. 

With  an  Introduction,  by  the  Rev.  Dr.  POTTER.  18mo,  Muslin. 
45  cents. 

This  manual  is  decidedly  the  best  which  has  yet  appeared  upon  the  subject,  and  is, 
as  it  were,  an  excellent  emblem  of  the  oratory  on  which  it  chiefly  dwells  :  admirable 
in  its  arrangement,  full  of  good  sense  in  much  of  its  detail,  with  a  felicitous  and  ju- 
dicious application  of  the  principles  of  Cicero  and  Quintilian  to  his  subject.— Qvar 
terly  Review. 

f^acfclcg's  Creates?  on 

Containing  the  latest  Improvements.    8vo,  Sheep.     $1  50. 

I  regard  it  as  a  very  valuable  accession  to  mathematical  science.  I  find  it  remark- 
ably full  and  complete. — E.  S.  S.NELL,  Professor  of  Mathematics,  Amherst  College, 
Massachusetts. 

I  deem  it  a  work  of  great  value  to  the  mathematical  student,  and  better  suited  to 
the  wants  of  private  learners,  and  all  others  who  wish  to  obtain  a  thorough  know] 
edge  of  the  science,  than  any  other  work  with  which  1  am  acquainted.— ELIJAH  A. 
SMITH,  Corresponding  Secretary  of  Queen's  County  Common  School  Association. 

I  have  examined  your  work,  and  am  highly  pleased  with  it.  Yonr  management  of 
the  roots  is  admirable,  as  also  of  many  other  topics  which:  I  might  mentioa.— N.  T 
CLARKE,  Canandaigua,  New  York.  ... 


12      WORKS    FOR    COLLEGES    AND    DISTRICT   SCHOOLS. 

SLoomte'g  ^Treatise  on 

8vo,  Sheep.     $1  25. 

Prof.  Loomis's  Treatise  on  Alg-ebra  is  an  excellent  elementary  woric.  It  is  sufli 
ciently  extensive  for  ordinary  purposes,  and  is  characterized  throughout  by  a  happy 
combination  of  brevity  and  clearness.  —  ALEXIS  CASWELL,  D.D.,  Professor  of  Math- 
ematics and  Natural  Philosophy  in  Brown  University, 

I  have  carefully  examined  Prof.  Loomis's  Algebra,  and  think  it  better  adapted  for 
a  text-book  for  college  students  than  any  other  I  have  seen.  —  C.  GILL,  Professor  of 
Mathematics  in  St.  Paul's  College. 

<£iarit's  32lemeuts  of  ^Igefcra: 

Embracing  also  the  Theory  and  Application  of  Logarithms  ;  together 
with  an  Appendix,  containing  Infinite  Series,  the  General  Theory 
of  Equations,  and  the  most  approved  Methods  of  resolving  the 
higher  Equations.  8vo,  Sheep  extra.  $1  00. 

The  object  of  this  treatise  is  to  present  to  the  student  a  full  and  systematic  text  . 
book  of  practical  and  theoretical  elementary  algebra.  Within  a  brief  compass  the  au- 
thor has  embraced  a  more  comprehensive  view  of  the  science  than  is  to  be  found  in 
any  similar  work.  These  features  can  not  fail  to  commend  the  book  to  the  notice  of 
teachers  ;  the  work,  indeed,  has  already  been  extensively  adopted  in  numerous  acad- 
emies and  schools  in  different  sections  of  the  country. 


s  Diatonic 

Plato  contra  Atheos.  Plato  against  the  Atheists  ;  or,  the  Tenth 
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Professor  Lewis  has,  in  this  work,  provided  a  rich  feast  both  for  the  student  and 
the  Christian.  —  New  York  Evangelist. 

See's  lElements  of  (&eolo<n>  for  ^Popular  gftse  ; 

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Uurfee's  ISssag  on  the  Sublime  antr  Beautiful. 

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•e  acknowledged  that  there  are  few  who  equal,  and  none  who  transcend  him. 


WORKS    FOR    COLLEGES    AND    DISTRICT    SCHOOLS.      13 

Elements  of  gftrmtstrg; 

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Muslin.     82  00. 

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research,  accurate  analysis,  and  profound  learning,  this  work  stands  unrivaled  among 
productions  of  its  class." 

23pttome  of  the  ®i8torg  of 


Being  the  Work  adopted  by  the  University  of  France  for  Instruction 
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$ojmlar 

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<£n  scorn's  Animal  JH  reliant  sin  airtr  Vhgsfolofig; 

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•work,  he  apprehends,  is  new  ;  but  the  peculiar  mode  of  teaching  them  is,  with  some 
variations,  that  which  has  been  so  successful  in  the  hands  of  Sir  Charles  Bell,  Dr. 
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of  Hftetorfc. 

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—Archbishop  Whately. 


14      WORKS    FOR    COLLEGES    AND    DISTRICT    SCHOOLS. 

Bouchariat's  22iemcntarg  ^Treatise  on 
J&echaiucs, 

Translated  from  the  French,  with  Additions  and  Emendations,  by 
Prof.  E.  H.  COURTENAY.  Plates.  8vo,  Sheep  extra.  $2  25. 

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vious mathematical  studies  will  enable  them  to  follow  out  the  most  useful  application. 
of  high  mathematics. 

f^emjiers  Grammar  of  the  German  Slanguage, 

Arranged  into  a  new  System  on  the  Principle  of  Induction.  2  vols. 
12mo,  half  Bound.  $1  75. 

(Class's  2Life  of  ^Washington, 

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Alexander  iu  a  golden  urn,  within  the  limits  of  this  little  but  sterling  volume. 

Brougham's  Pleasures  antr  ^trfeantages  of 
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A  work  singularly  rich  in  all  that  can  touch  the  heart  and  interest  the  imagination 
-Athen 


